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CarlShulman comments on Yes, Virginia, You Can Be 99.99% (Or More!) Certain That 53 Is Prime - Less Wrong
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This only talks about the probability of the evidence given the truth of the hypothesis, but ignores the probability of the evidence given its falsity. For a variety of reasons, fake claims of miracles are far more common than fake TV announcements of the lottery numbers, which drastically reduces the likelihood ratio you get from the miracle claim relative to the lotto announcement.
The specific miracle also has lower prior probability (miracles are possible+this specific miracle's details), but that's not the only issue.
Even if true announcments are just 9 times more likely than false announcements, then a true announcment should raise your confidence that the lottery numbers were 4 2 9 7 9 3 to 90%. This is because the probability P (429783 announced | 429783 is the number) is just the probability of a true announcement, but the probability P( 429783 announced | 429783 is not the number) is the probability of a false announcement, divided by a million.
A false announcer would have little reason to fake the number 429793. This already completely annihilates the prior probability.
Actually, I'd consider it fairly important. It's one reason the probabilities ought to get very small very fast, but if you're reluctant to assign less than one in a million odds...
I think it's important to grasp the general principle under which a person telling you that this week's winning lotto numbers are some particular sequence is stronger evidence than their telling you a miracle took place. It offers a greater odds ratio, because they're much less likely to convey a particular lottery number in the event of it not being the winning one than they are to convey a miracle story in the event that no miracle occurred (even people who believe in miracles should be able to accept that miracles have a very high false positive rate if they believe that miracles only occur within their own religion.)
To illustrate: Suppose you're checking the lottery results online, and you see that you won, and you're on your laptop at the house of a friend who knows what lottery numbers you buy and who has used his wi-fi to play pranks on guests in past. Suddenly the evidence doesn't fare so well against that million-to-one prior.
This reminds me of reading about the Miracle of the Sun (http://en.wikipedia.org/wiki/Miracle_of_the_Sun) in The God Delusion and in a theist's response. I found Dawkins fairly unpersuasive; the many agreeing testimonials weren't enough to overcome the enormous prior improbability, but they were still disconcertingly strong evidence. The theists' response cleared this up by giving historical background that Dawkins omitted. Apparently, the miracle was predicted in advance by three children and had become a focal point in the tensions between the devout and the secular. Suddenly, it was not at all surprising that the gathered crowd witnessed a miracle.
So I'd agree that miracles often have probability of under one in a million, but it's also vitally important to understand the effect of motivation on the likelihood of the evidence. If I thought every testimony to every reported miracle was based on unbiased reporting of fact, I'd have to conclude that many of them happened (caused by aliens messing with us or something).
Craig is just purposely conflating the likelihood of a particular result and the likelihood of given the declaration of a result by the lottery officials, that result being true.
If you and I are flipping coins for a million dollars, it's going to take a lot of convincing evidence that I lost the coin flip before I pay up. You just cannot flip the coin in another room where I can't even see, and then expect me to pay up because, well, the probability of heads is 50% and I shouldn't be so surprised to learn that I lost.
Therefore, the actual likelihood of a particular set of lottery numbers is totally irrelevant in this discussion.
In any case, the only kind of "evidence" that we have been presented for miracles has always been of the form "person X says Y happened', which has been known as hearsay and dealt with without even bothering with probability theory.