When you've eliminated the impossible, if whatever's left is sufficiently improbable, you probable haven't considered a wide enough space of candidate possibilities.
Seems fair. The Holmes saying seems a bit funny to me now that I think about it, because the probability of an unlikely event changes to become more likely when you've shown that reality appears constrained from the alternatives. I mean, I guess that's what he's trying to convey in his own way. But, by the definition of probability, the likelihood of the improbable event increases as constraints appear preventing the other possibilities. You're going from P(A) to P(A|B) to P(A|(B&C)) to.. etc. You shouldn't be simultaneously aware that an event is impr...
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