In every case of an alleged miracle, it is always more likely that it has a rational explanation than not, even if we do not know what that rational explanation is. For instance, let's say you see someone "rise from the dead". Pretty impressive. But given that all experience tells us this is impossible, no matter how striking your experience, it will always be more likely that you were somehow tricked or deceived. After all, we know the brain plays all sorts of tricks on us, and others play tricks on our brains....
So what Hume's argument boils down to, then, is that we have never had any good reason to believe that a miracle has occurred, and nor are we likely to.
This, however, is not quite right, and we find here a misstep that we found in different form in the other discussion. There Baggini took Hume's claims about laws of nature, which in Hume are claims about psychology, about subjective features of reasoning, and interpreted them as claims about objective fact. So Hume's psychologically forceful regularities became Baggini's delineators of real physical possibility. Here we find a similar transposition. Hume might believe, but he does not argue that "we have never had any good reason to believe that a miracle has occurred." Nor is his claim that "In every case of an alleged miracle, it is always more likely that it has a rational explanation than not, even if we do not know what that rational explanation is." Hume's argument does not depend on dubious assessments of the 'likelihood' that an actual event has a non-miraculous explanation. Quite the contrary: his argument is about the likelihood that testimony is bad; and his argument in Part II basically boils down to the claim that we know that religious people are likely both to lie and be deceived where religious matters are involved. Thus whenever someone tells you about a miracle for religious purposes, there will always be a doubt about whether they are lying or gullible. There are ways to compensate for this sort of doubt, which Hume addresses, but, Hume argues, no testimony for religious miracles has ever fulfilled the required conditions. Therefore testimony for religious miracles always falls short of the force of proof; and since the laws of nature are supported by the force of proof, and Hume has argued in Part I that testimony for miracles and induction supporting the laws of nature are opposed, the laws of nature will always win out, as having the superior force. (At least, in reasonable moments. The superiority here is psychological, not logical, which raises the question of how people could believe in miracles anyway, since it seems that the laws of nature would always have superior force. On Hume's view things like transient passions, taste for novelty, prejudices, etc., can raise the psychological force of something in inconsistent, unstable, or arbitrary ways. So it seems that Hume is committed to saying that genuine belief in a miracle is a case where the psychological force of the idea of the miracle is artificially increased by associationg with passion-inducing factors. And indeed this seems to be his idea; he holds, for instance, that organized religions make use of a lot of these inducers of psychological force, and that certain passions like surprise can under certain circumstances make us believe things we wouldn't otherwise believe.) Thus it is not the mere fact that another explanation is more likely that is driving the argument; it has to be combined with Hume's claims about the laws of nature, or there is no argument.
What Hume's argument does not show, and does not purport to show, and should not try to show given that Hume does not make a sharp distinction between the very extraordinary and the miraculous, is what would happen if we experienced a miracle ourselves. Hume's argument is dependent on claims about testimony and how human beings receive it. It has nothing to do with the actual miracles themselves, and, in fact, Hume immediately faces the problem of how you could possibly justify any revision of what seem to be laws of nature on testimonial grounds. The ongoing problem Hume faces throughout the essay is how to rule out testimony as a good source for believing a miracle without ruling out testimony as a means for sharing startling genuine discoveries. Hume's skepticism has no means for ruling out miracles a priori, and it has to move very carefully in order to avoid suppressing testimony too sharply, because testimony is essential to our scientific understanding of the world, and is the reason why we don't have to do every experiment ourselves. If we could rule out miracles a priori, we wouldn't need Hume's arguments; we would know that anything that defied universal commonsense principles is false. But that would also rule out unique natural causes. But Hume is an empiricist, not a rationalist; he doesn't want to rule anything out a priori, and even if he did he wouldn't want to rule out unique natural causes before any investigation had even been undertaken. And one also doesn't want to rule out any revision, based on scientific or historical study, of our view of how the world fundamentally works. Hume has to consider this issue. And he does consider it, in the passage about the hypothetical eight days of darkness. It would be possible to accept on testimony the occurrence of a thoroughly extraordinary event under certain conditions -- namely, conditions where the testimony was very good and where the deviation from the laws of nature was itself conformable to other laws of nature (and thus borrowed force from them).
So that's really what's going on in Hume's argument. And the argument depends crucially on three things: Hume's account of the laws of nature, Hume's claims about counterpoise (i.e., his psychology of belief), and Hume's claims about religious testimony. And these are three things that very few people, even those sympathetic to Hume, actually accept. Baggini himself deviates from Hume's account of laws of nature. Baggini seems to accept the counterpoise principle as "obvious"; but it has more usually been thought perplexing, and requires a particular notion of belief, as forcefulness of idea transmissible by association, that is rarely held and, indeed, has a long history of being mocked as silly. And indeed, Baggini is very ambiguous about whether he takes it to be a psychological mechanism, as Hume does, or as a normative principle, which makes the argument somewhat different from Hume's. Baggini says some things that are naturally interpreted one way, and some things that are naturally interpreted the other way. The only one of the three that is in any sense widely accepted is the claim that religious testimony tends to be pernicious; but this on its own is not enough to run the argument.
Again we find that Baggini's argument makes use of a few comments by Hume, but in fact appears to be a different argument entirely. It's an interesting sort of argument, but it's impossible to say whether it begs the question unless we have a better idea of what Baggini's account of the greater likelihood of "rational explanation" is. Obviously, for instance, a type of explanation may be more likely in general but less likely in particular kinds of cases; Baggini's use of the claim has to mean that there are no relevant possible cases where the alternative would be more likely. But it's hard to see how one would go about defending such a claim without simply assuming that miracles can't happen. Lacking Baggini's own defense of this point, we are left unclear about how to evaluate the argument even on its own terms, without rebuttal of any of its points.