Huh, I must be slowed down because it's late at night... P(A|A) is the simplest case of all. P(x|y) is defined as P(x,y)/P(y). P(A|A) is defined as P(A,A)/P(A) = P(A)/P(A) = 1. The ratio of these two probabilities may be 1, but I deny that there's any actual probability that's equal to 1. P(|) is a mere notational convenience, nothing more. Just because we conventionally write this ratio using a "P" symbol doesn't make it a probability.

## Comments (116)

OldHuh, I must be slowed down because it's late at night... P(A|A) is the simplest case of all. P(x|y) is defined as P(x,y)/P(y). P(A|A) is defined as P(A,A)/P(A) = P(A)/P(A) = 1. The

ratioof these two probabilities may be 1, but I deny that there's anyactualprobability that's equal to 1. P(|) is a mere notational convenience, nothing more. Just because we conventionally write this ratio using a "P" symbol doesn't make it a probability.But it does obey the Kolmogorov axioms (it can't be greater than 1 for instance); that seems important.