[tex]P(X\mid Y)[/tex] is the probability that [tex]X[/tex] occurs given that [tex]Y[/tex] occurs, i.e. the conditional probability of [tex]X[/tex] occurring conditioned on [tex]Y[/tex]. By definition,
[tex]P(X\mid Y)=\dfrac{P(X\cap Y)}{P(Y)}[/tex]
