I am reading a paper on privacy that says we can model something as an arbitrary probabilistic function from $X^M \to X^M$. I'm trying to figure out what exactly that means. I saw another paper that defined a probabilistic function as a function $\mathcal{F}:X \times Y \to [0, 1]$ that satisfied the condition $$\forall x \in X: \sum_{y \in Y} \mathcal{F}(x, y) \leq 1.$$ But that definition doesn't seem to make sense if the function can take on values in the space $X^M$ where $X$ is an arbitrary set of objects. So what exactly are probabilistic functions?
Thanks so much!