The extension to the situation calculus presented by Bacchus et al. formalizes the concept of noisy actions and shows how an agent can update its beliefs, which are modeled probabilistically, when relying on noisy sensors and effectors. The extensions of Scherl and Levesque and Shapiro et al. also model knowledge and belief. While assuming noiseless actions and dealing with boolean beliefs, these frameworks support properties of knowledge and belief such as introspection about current and past beliefs. Here, it is shown how such properties of belief can be formalized and supported in the probabilistic Bacchus et al. extension. In addition, the concept of sensor coarseness is introduced and it is shown how it can be modeled in the Bacchus et al. framework. Finally, it is shown that the Bacchus et al. framework can function in a way which is equivalent to using conditional probability densities to combine noisy sensor readings.