Posterior Probability

Posterior Probability of a random event is the resulting probability after taking into account, the relevant evidence.

Example: if $p(\theta)$ is the probability of occurence of $\theta$, then after observing an evidence $X$, the posterior probability of $\theta$ will become $p(\theta | X)$.

In this example $p(\theta)$ itself is called the prior belief or probability. And the reverse, $p(X | \theta)$ is called the likelihood.