Electrical power systems play a critical role in spacecraft and aircraft, and they exhibit a rich variety of failure modes. This paper discusses electrical power system fault diagnosis by means of probabilistic techniques. Specically, we discuss our development of a diagnostic capability for an electrical power system testbed, ADAPT, located at NASA Ames. We emphasize how we have tackled two challenges, regarding modelling and real-time performance, often encountered when developing diagnostic applications. We carefully discuss our Bayesian network modeling approach for electrical power systems. To achieve real-time performance, we build on recent theoretically well-founded developments that compile a Bayesian network into an arithmetic circuit. Arithmetic circuits have low footprint and are optimized for embedded, real-time systems such as spacecraft and aircraft. We discuss our probabilistic diagnostic models developed for ADAPT along with successful experimental results.