Summary: The differential equations governing the probability distribution of events distributed over a multidimensional domain are derived. They are a generalization of the equations governing the probability distribution in a time series. Let \(f_r(x,y)\,dx\,dy\) be the chance that an event will occur in the domain \(\,dx\,dy\) when \(r\) events have already occurred in the domain \((0,x;0,y)\). The equations which are derived then govern the set of functions \(W_n(x,y)\), where \(W_n\) is the chance that \(n\) events occur in the domain \((0,x;0,y)\). The problem of solving them reduces to the solution of a sequence of first-order ordinary equations, but these are exact, so the solution is merely a matter of quadratures. The general solution is written, and a few simple illustrations are given.