Probability theory defines how we would ideally reason in the face of uncertainty, if we had the time, the computing power, and the self-control. Given some background knowledge (priors) and a new piece of evidence, probability theory uniquely defines the best set of new beliefs (posterior) I could adopt. Likewise, decision theory defines what action I should take based on my beliefs. For any consistent set of beliefs and preferences I could have about Bob, there is a decision-theoretic answer to how I should then act in order to satisfy my preferences.
