If A and B are events (see sample space), and P(B)>0, the conditional probability of A given B is defined by
or equivalently
If P(A)>0 also, then P(A ∩ B)=P(A)×P(B|A), so
The ‘A|B’ notation was introduced by Jeffreys and popularized by Feller. See also bayes's theorem; independent events.