We present in this paper a case study of the probabilistic approach to model-based diagnosis. Here, the diagnosed system is a real-world electrical power system (EPS), i.e., the Advanced Diagnostic and Prognostic Testbed (ADAPT) located at the NASA Ames Research Center. Our probabilistic approach is formally well founded and based on Bayesian networks (BNs) and arithmetic circuits (ACs). We pay special attention to meeting two of the main challenges often associated with real-world application of model-based diagnosis technologies: model development and real-time reasoning. To address the challenge of model development, we develop a systematic approach to representing EPSs as BNs, supported by an easy-to-use specification language. To address the real-time reasoning challenge, we compile BNs into ACs. AC evaluation (ACE) supports real-time diagnosis by being predictable, fast, and exact. In experiments with the ADAPT BN, which contains 503 discrete nodes and 579 edges and produces accurate results, the time taken to compute the most probable explanation using ACs has a mean of 0.2625 ms and a standard deviation of 0.2028 ms. In comparative experiments, we found that, while the variable elimination and join tree propagation algorithms also perform very well in the ADAPT setting, ACE was an order of magnitude or more faster.