Most object tracking approaches either assume that the number of objects is constant, or that information about object existence is provided by some external source. Here, we show how object existence can be rigorously integrated within the Bayesian single and multiple object tracking framework. We provide a general treatment that impacts as little as possible on existing tracking algorithms, so that software can be reused, and that allows implementation with Kalman Filters, Extended Kalman Filters, Particle Filters, etc. We apply the proposed framework to colour-based tracking of multiple objects.