We propose a mathematical model of the Path Integration (PI) process. Its core assumption is that orientations of a path are summarized by circular probability distributions. We compare our model with classical, deterministic models of PI and find that, although they are indistinguishable in terms of information encoded, the probabilistic model is more parsimonious when considering navigation strategies. We show how sensory events can enrich the probability distributions memorized, resulting in a continuum of navigation strategies, from PI to stimulus-triggered response. We analyze the combination of circular probability distributions (e.g., multicue fusion), and demonstrate that, contrary to the linear case, adding orientation cues does not always increase reliability of estimates. We discuss experimental predictions entailed by our model.