Probability kinematics is the theory of how subjective probabilities change with time, in response to certain constraints (accepted by the subject in response to his experience or incoming information). Transformations — rules for updating one's probabilities — which have been described and to some extent accepted in the literature, include (in increasing order of generality): conditionalization, Jeffrey conditionalization, and INFOMIN (relative information minimizing). The present paper investigates the general problem. By an argument purely based on symmetry considerations it is demonstrated that conditionalization and Jeffrey conditionalization are the unique admissible rules for the cases to which they apply. The general problem is thereby reduced to a sequence of two operations, the second a Jeffrey conditionalization and the first a determination of posterior odds on some partition. In Section 2 we give a new deduction of INFOMIN from a simple postulate; in Section 3 a rival rule (MTP) derived from an analogy to quantum mechanics. The Appendix presents some preliminary comparisons.