Here's my take on the meaning of the slogan: Extraordinary Claims Require Extraordinary Evidence. (I don't know if other nonbelievers would agree with this.) An extraordinary claim is a claim that an improbable event occurred. An example is a miracle. Since a miracle is a violation of a law of nature it does not happen very often, possibly never. We can estimate a highest possible value for the probability of some miracle occurring e.g one in a billion for a person rising from the dead. (Say if approximately out of every billion people that have died there is one alleged claim of resurrection.) Extraordinary evidence for an extraordinary claim would be evidence which if the claim were not true, then the probability of the evidence itself would be a lot lower than that of the extraordinary claim being true. For example if testimony to a miracle was given and the likelihood of such testimony occurring was say one in a trillion if the miracle did not actually occur. (Thus a believer might argue that approximately out of every trillion false claims made there is at most one which is endorsed by a person willing to die for the claim.) If the probabilities involved cannot be compared then no case can be made.
By Peter Hawkins on The onus of miracles on 12/31/10
Is it improbable that a poker player had five royal flushes in a row? Well, that’s highly improbably if the deck is randomly shuffled. If, on the other hand, the dealer is a card sharp, then it may be highly probable (even inevitable) that the player had five royal flushes in a row.
So you really can’t say, in the abstract, what is probable or improbable. That depends on other variables, known or unknown.