In Bayesian inference, a posterior probability of a value x of a random variable X given a context a value y of a random variable Y, P(X = x | Y = y), is the probability of X assuming the value x in the context of Y = y. It contrasts with the prior probability, P(X = x), the probability of X assuming the value x in the absence of additional information.
For example, it may be that the prevalence of a particular form of cancer, exoma, in the population is 0.1%, so the prior probability of exoma, P(exoma = true), is 0.001. However, assume 50% of people who have skin discolorations of greater than 1 cm width (sd > 1cm) have exoma. It follows that the posterior probability of exoma given sd > 1cm, P(exoma = true | sd > 1cm = true), is 0.500.