I'm embarassed to bring this up again, because I seem to quote steven0461 too often--but, in something close to his words; "When you have eliminated the impossible, whatever remains is likely more improbable than an error in one of your impossibility proofs."

I reject that entirely," said Dirk, sharply. "The impossible often has a kind of integrity to it which the merely improbable lacks. How often have you been presented with an apparently rational explanation of something which works in all respects other than one, which is just that it is hopelessly improbable? Your instinct is to say, `Yes, but he or she simply wouldn't do that.'"

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...Or you've just missed something. If all you're left with is improbable you notice that you are confused. I've always thought that quote was off.

Then again, Sherlock never did miss anything.

There is no evidence that is so strong that it will justify a statement no matter how improbable you initially considered it. Thus, as Oscar points out, this quote is off.

In Bayes/Pearl terminology, knowledge of an effect destroys the causes' independence (d-connects them), and ruling out a cause shifts probability onto the remaining causes.

As a rationality quote, "... must contain the truth" would have been better.