Do miracles defy the laws of probability?

Your assumption that “by definition, a miracle is more improbable than any natural explanation” is false. While we may be able to compare the probability or improbability of natural events, we can’t make such comparisons with supernatural events because we have no way to calculate from natural events the likelihood of a supernatural event. Natural events can tell us only about the likelihood (or unlikelihood) of another natural event.

Of course, experience teaches us that miracles happen infrequently. Whether this is because God chooses rarely to intervene in the natural order or we lack the prerequisite faith, we can’t say. What we do know is that the frequency of miracles isn’t decided by what happens in the natural order, but by the sovereign will of God. We can no more argue for the improbability of miracles based on the predictability of the natural order than we can predict a change in the bus schedule by considering when the bus usually arrives.