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We extend the Eindhoven quantifier notation to elementary probability theory by adding "distribution comprehensions" to it. Even elementary theories can be used in complicated ways, and this occurs especially when reasoning about computer programs: an instance of this is the multi-level probabilistic structures that arise in probabilistic semantics for security. Our exemplary case study in this article is therefore the probabilistic reasoning associated with a quantitative noninterference semantics based on Hidden Markov Models of computation. But we believe the proposal here will be more generally applicable than that, and so we also revisit a number of popular puzzles, to illustrate the new notation's wider utility.