Conditional probability

Conditional probability is the probability of an event given that another event has already occurred. Write it as $P(A|B)$, read "the probability of $A$ given $B$." The formula is $P(A|B)=\frac{P(A\cap B)}{P(B)}$, provided $P(B)>0$. The numerator is the probability that both events happen; the denominator restricts attention to cases where $B$ happens. In words, shrink the sample space to only outcomes in $B$, then measure how many of those also lie in $A$.