it actually wouldn't take all that much evidence to convince us that, for example, "the numbers chosen in last night's lottery were 4, 2, 9, 7, 8 and 3." The correct response to this argument is to say that the prior probability of a miracle occurring is orders of magnitude smaller than mere one in a million odds.

That doesn't seem right. If somebody tries to convince me that the result of a fair 5 number lottery is 1, 2, 3, 4, 5 I would have a much harder time believing it, but not because the probability is less then one in a million. I think the correct answer is that if the outcome of the lottery wasn't 4, 2, 9, 7, 8, 3 it is very unlikely anybody would try to convince me that the result was exactly that one.

[assume outcome is 4, 2, 9, 7, 8, 3]

Whereas P(outcome) is 1/1 000 000, P(outcome|they tell you the outcome is outcome) is much higher because P(they tell you the outcome is outcome|not outcome) is so much lower then P(they tell you the outcome is outcome|outcome)