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You can't mean what you are asking. Someone getting eight royals in a row might be favored to happen exactly once.

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By the way I meant exactly what I was asking. Your point with the royals translates to:

"What is the probability that intelligent life evolves on some planet, they go on to invent exactly the game of poker, and then one day someone gets some absurdly crazy sequence of hands, and furthermore they die off before it happens again?"

I'd call this a miracle. Hence, probability zero.

"Now, GIVEN that humans HAVE invented poker, what is the likelihood that some crazy sequence occurs exactly once?"

Well, here we already believe in a miracle, since we have actually witnessed humans invent poker, and we see it all around us. So now the answer is probably 1.

My point was ultimately that probability is useless with respect to the likelihood of miracles. What is the chance of all of New York City turning out exactly the same, given that the conditions in the year 10000 BC were exactly as they were, except for some "irrelevant" differences? Zero. But this doesn't change the fact that we do actually observe an actual New York City, and it is the way it is.

Who woulda thunk it?