Dopamine release in the nucleus accumbens has been hypothesized to signal reward prediction error, the difference between observed and predicted reward, suggesting a biological implementation for reinforcement learning. Rigorous tests of this hypothesis require assumptions about how the brain maps sensory signals to reward predictions, yet this mapping is still poorly understood. In particular, the mapping is non-trivial when sensory signals provide ambiguous information about the hidden state of the environment. Previous work using classical conditioning tasks has suggested that reward predictions are generated conditional on probabilistic beliefs about the hidden state, such that dopamine implicitly reflects these beliefs. Here we test this hypothesis in the context of an instrumental task (a two-armed bandit), where the hidden state switches repeatedly. We measured choice behavior and recorded dLight signals reflecting dopamine release in the nucleus accumbens core. Model comparison based on the behavioral data favored models that used Bayesian updating of probabilistic beliefs. These same models also quantitatively matched the dopamine measurements better than non-Bayesian alternatives. We conclude that probabilistic belief computation plays a fundamental role in instrumental performance and associated mesolimbic dopamine signaling.