Probability theory has come to play a central role in recent discussions about belief, once thought to be too nuanced to ever admit quantitative analysis. The lottery paradox poses a major hurdle to this approach, demonstrating how, together with some highly plausible assumptions, any probabilistic threshold for belief less than one is bound to lead to incon- sistent beliefs. We aim to defend a probabilistic theory of belief by taking up an idea of Leitgeb (2017). Our approach focuses on the role of context in the formation of beliefs; and in particular, on the alternative beliefs considered by an agent. To do so, we appeal to inquisitive semantics as a background framework. Inquisitive semantics seeks to formalise the role of questions in discourse, thereby furnishing a new perspective of the meaning of a sentence in terms of the questions it answers. We give an account for several aspects of questions in a framework based on Leitgeb’s theory, such as the difficulty of questions.