Human and non-human animals estimate the probabilities of events spread out in time. They do so on the basis of a record in memory of the sequence of events, not by the event-by-event updating of the estimate. The current estimate of the probability is the byproduct of the construction of a hierarchical stochastic model for the event sequence. The model enables efficient encoding of the sequence (minimizing memory demands) and it enables nearly optimal prediction (The Minimum Description Length Principle). The estimates are generally close to those of an ideal observer over the full range of probabilities. Changes are quickly detected. Human subjects, at least, have second thoughts about their most recently detected change, revising their opinion in the light of subsequent data, thereby retroactively correcting for the effects of garden path sequences on their model. Their detection of changes is affected by their estimate of the probability of such changes, as it should be. Thus, a sophisticated mechanism for the perception of probability joins the mechanisms for the perception of other abstractions, such as duration, distance, direction, and numerosity, as a foundational and evolutionarily ancient brain mechanism.