Our expectation of an event such as a visual stimulus clearly depends on previous experience, but how the brain computes this expectation is currently not fully understood. Because expectation influences the time to respond to a stimulus, we arranged for the probability of a visual target to suddenly change and found that the time taken to make an eye movement to it then changed continuously, eventually stabilizing at a level reflecting the new probability. The time course of this change can be modeled making a simple assumption: that the brain discounts old information about the probability of an event by a factor λ, relative to new information. The value of λ presumably represents a compromise between responding rapidly to genuine changes in the environment and not prematurely discarding information still of value. The model we propose may be implemented by a very simple neural circuit composed of only a few neurons.