For two jointly distributed random variables X and Y the conditional distribution of Y given X is the distribution of Y when X takes particular values. For discrete random variables it is given by
P[Y = y | X = x] = P[X = x, Y = y]/P[X = x].
For continuous random variables, the conditional density function is given by
f(y | x) = f(x, y)/f(x)
where f(x, y) is the joint density function, and f(x) is the marginal density function of X.