How do people make inferences from complex patterns of evidence across diverse situations? What does a computational model need in order to capture the abstract knowledge people use for everyday reasoning? In this paper, we explore a novel modeling framework based on the probabilistic language of thought (PLoT) hypothesis, which conceptualizes thinking in terms of probabilistic inference over compositionally structured representations. The core assumptions of the PLoT hypothesis are realized in the probabilistic programming language Church (Goodman et al., 2008). Using "ping pong tournaments" as a case study, we show how a single Church program concisely represents the concepts required to specify inferences from diverse patterns of evidence. In two experiments, we demonstrate a very close fit between our model's predictions and participants' judgments. Our model accurately predicts how people reason with confounded and indirect evidence and how different sources of information are integrated.