Electrical power systems play a critical role in spacecraft and aircraft. This paper discusses our development of a diagnostic capability for an electrical power system testbed, ADAPT, using probabilistic techniques. In the context of ADAPT, we present two challenges, regarding modelling and real-time performance, often encountered in real-world diagnostic applications. To meet the modelling challenge, we discuss our novel high-level specification language which supports auto-generation of Bayesian networks. To meet the real-time challenge, we compile Bayesian networks into arithmetic circuits. Arithmetic circuits typically have small footprints and are optimized for the real-time avionics systems found in spacecraft and aircraft. Using our approach, we present how Bayesian networks with over 400 nodes are auto-generated and then compiled into arithmetic circuits. Using real-world data from ADAPT as well as simulated data, we obtain average inference times smaller than one millisecond when computing diagnostic queries using arithmetic circuits that model our real-world electrical power system.