The applicability of Bayesian conditionalization in setting one's posterior probability for a proposition, a, is limited to cases where the value of a corresponding prior probability, P PRI (a|โงE), is available, where โงE represents one's complete body of evidence. In order to extend probability updating to cases where the prior probabilities needed for Bayesian conditionalization are unavailable, I introduce an inference schema, defeasible conditionalization, which allows one to update one's personal probability in a proposition by conditioning on a proposition that represents a proper subset of one's complete body of evidence. While defeasible conditionalization has wider applicability than standard Bayesian conditionalization (since it may be used when the value of a relevant prior probability, P PRI (a|โงE), is unavailable), there are circumstances under which some instances of defeasible conditionalization are unreasonable. To address this difficulty, I outline the conditions under which instances of defeasible conditionalization are defeated. To conclude the article, I suggest that the prescriptions of direct inference and statistical induction can be encoded within the proposed system of probability updating, by the selection of intuitively reasonable prior probabilities.