Final answer:
The posterior probability in the equation is p(b/a), and the prior probability is p(b); the equation represents Bayes' theorem.
Step-by-step explanation:
The equation presented in the question is a representation of Bayes' theorem. In the equation p(b/a) = (p(a/b) p(b)) / p(a), the term p(b/a) is referred to as the posterior probability, which is the probability of event b occurring given that event a has occurred. The term p(b) is known as the prior probability, which is the probability of event b before considering the evidence (event a).
The term p(a/b) is the likelihood, which is the probability of event a occurring given b. Finally, p(a) is the total probability of event a. Bayes' theorem is fundamental in the Bayesian paradigm, and it updates our beliefs about the likelihood of an event based on new evidence.