Quantum correlations which violate Bell inequalities cannot be recovered using classical random variables that are assigned to a certain background causal structure. Moreover, Tsirelson's bound demonstrates a separation between quantum correlations and those achievable by an arbitrary no-signalling theory. However, one can consider causal structures other than that of the usual Bell setup. We investigate quantum correlations from this more general perspective, particularly in relation to Pearl's influential work on causality and probabilistic reasoning, which uses the formalism of Bayesian networks. We extend this formalism to the setting of generalised probabilistic theories, and show that the classical d-separation theorem extends to our setting. We also explore how classical, quantum and general probabilistic theories separate for other causal structures; and also when all three sets coincide.