Goal recognition aims to infer an agent’s goal from partial observations of its behaviour. Existing approaches derive likelihoods from the costs of plans consistent with observations, often relying on trajectory-level reasoning and Boltzmann-rational models. In this work, we adopt a distributional perspective in which both goals and observations are represented as distributions over an outcome domain. We show that likelihoods and posterior probabilities can be characterised through identities that relate GR to divergences between observation-induced and goal-intended distributions. These identities expose a common structure across inference regimes, unifying probabilistic (sum-product) and optimisation-based (max-product) formulations. Our formulation captures cost-based goal recognition as a special case, and provides a common perspective alongside related approaches such as inverse reinforcement learning and Boltzmann-rational models of behaviour. By deriving existing models in a more general probabilistic setting, the framework offers an abstract account of goal recognition and formally situates known results within a broader class of inference problems over structured distributions.