As examples such as the quizmaster problem and the 3-prisoners puzzle show, applying conditioning to update a probability distribution on a `naive space', which does not take into account the protocol used, can often lead to counterintuitive results. We give a detailed explanation of this phenomenon. A criterion known as CAR (`coarsening at random') in the statistical literature characterizes when `naive' conditioning in a naive space works. We provide two new characterizations of CAR. First we show that in many situations, CAR essentially *cannot* hold, so that naive conditioning must give the wrong answer. Second, we provide a procedural characterization of CAR, giving a randomized algorithm that generates all and only distributions for which CAR holds. Both results complement earlier work by Gill, Van der Laan and Robins. We also consider more generalized notions of update such as Jeffrey conditioning and minimizing relative entropy (MRE), generalizing and interconnecting previous results obtained in the literature on CAR and MRE. joint work with Joe Halpern, Cornell University, Ithaca, NY.