We introduce and characterize inertial updating of beliefs. Under inertial updating, a decision maker (DM) chooses a belief that minimizes the subjective distance between their prior belief and the set of beliefs consistent with the observed event. Importantly, by varying the subjective notion of distance, inertial updating provides a unifying framework that nests three different types of belief updating: (i) Bayesian updating, (ii) non-Bayesian updating rules, and (iii) updating rules for events with zero probability, including the conditional probability system (CPS) of Myerson (1986a,b). We demonstrate that our model is behaviorally equivalent to the Hypothesis Testing model (HT) of Ortoleva (2012), clarifying the connection between HT and CPS. We apply our model to a persuasion game.