Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data likelihoods for a test example from its original class posteriors and dataset priors. Given the recovered likelihoods and a set of new priors, the posteriors can be re-computed using Bayes' Rule to reflect the influence of the new priors. The method is simple to compute and allows a dynamic update of the original posteriors.