We focus on systems where trust in a computational entity is interpreted as the expectation of certain future behaviour based on behavioural patterns of the past, and concern ourselves with the foundations of such probabilistic systems. In particular, we aim at establishing formal probabilistic models for computational trust and their fundamental properties. In the paper we define a mathematical measure for quantitatively comparing the effectiveness of probabilistic computational trust systems in various environments. With this foundation in place, we formalise a general notion of information about past behaviour, based on event structures. This yields a flexible trust model where the probability of complex protocol outcomes can be assessed.