If you store a specification for a probability distribution and give that specification a name, it can behave like a function in that it can be sampled for a scalar output. It can behave like a variable in that you can assign it to a new variable name, play with it as you would anything else in a programming language. And a linear system, perhaps overdetermined, is but one of many ways that the specification can be defined under the hood.

The fact that one can play with complicated nested probability distributions that unify these concepts, as one would play with dolls in a dollhouse, is the point!