The prevalence of electronic trading has radically changed the market structure in several asset classes, most notably in equities and futures. All market participants in a public electronic venue contribute to price formation by adding and removing liquidity in a limit order book, which ranks the buy and sell orders. In this article, the authors first compute empirically average price moves and waiting times conditional on the state of the order book. Then the probabilities for favourable price moves -- down for posting at the bid, up for posting at the ask -- and unfavourable price moves, as well as trade occurrences, can be computed using a stochastic model for diffusion in three dimensions. Bid and ask queues, and the timing of the near-side trade arrivals, are modelled and supplied with suitable boundary conditions. The solution of the model takes the form of a two-dimensional Fourier-Laplace expansion with fast convergence away from the boundary, the coefficients for which can be obtained by transforming boundary conditions into a matrix equation.