Probabilistic expert systems are intended to provide reasoned guidance in complex environments characterized by extensive uncertainty. An explicit `causal' model is constructed for the process being observed, in which an acyclic directed graph is used to express conditional independence assumptions about variables, and probability assessments specify a full joint probability distribution. The resulting graphical structure can cope with a range of issues that arise in realistic modelling. Here we consider a particular example of assessing the chance that a suspected adverse reaction is due to a particular drug under suspicion. The background biological knowledge provides an appropriate model and probability assessments are obtained from expert microbiologists. The model allows a variety of interpretations for `causality'. Details of the graphical and computational algorithms used to perform efficient calculations of conditional probabilities on complex graphical structures are provided and illustrated with the example. Further developments should allow updating of the risk parameters in the light of a series of case reports, and may form the basis for a flexible expert system for causality assessment and post-marketing surveillance.