Logics of knowledge and belief are often too static and inflexible to be used on real-world problems. In particular, they usually offer no concept for expressing that some course of events is more likely to happen than another. We address this problem and extend CTLK (computation tree logic with knowledge) with a notion of plausibility, which allows for practical and counterfactual reasoning. The new logic CTLKP (CTLK with plausibility) includes also a particular notion of belief. A plausibility update operator is added to this logic in order to change plausibility assumptions dynamically. Furthermore, we examine some important properties of these concepts. In particular, we show that, for a natural class of models, belief is a KD45 modality. We also show that model checking CTLKP is PTIME-complete and can be done in time linear with respect to the size of models and formulae.