DEFINITION of 'Posterior Probability'
The revised probability of an event occurring after taking into consideration new information. Posterior probability is normally calculated by updating the prior probability by using Bayes' theorem. In statistical terms, the posterior probability is the probability of event A occurring given that event B has occurred.
BREAKING DOWN 'Posterior Probability'
Bayes' theorem can be used in many applications, such as medicine, finance and economics. In finance, Bayes' theorem can be used to update a previous belief once new information is obtained. For instance, suppose you believed the stock market had a 50% chance of going down over the next year. You can update this prior probability if you get new information regarding interest rates, GDP or unemployment, to obtain a posterior probability.

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A Priori Probability
Probability calculated by logically examining existing information. ... 
Joint Probability
A statistical measure where the likelihood of two events occurring ...

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