What you do to your beliefs, opinions and cognitive structure when new information comes along.
[[Cox's theorem]] says, roughly, that if your beliefs at any given time take the form of an assignment of a numerical "plausibility score" to every proposition, and if they satisfy a few plausible axioms, then your plausibilities must effectively be probabilities obeying the usual laws of probability theory, and your updating procedure must be the one implied by [[Bayes' theorem]].