How to visualize probability distributions in terms of sets - joint and marginal? Let there be two sets, $\mathcal{X},\mathcal{Y}$, both finite, and they represent the set of values that the discrete random variables, $X,Y$ can take. $\mathcal{P}_{Y|X}$ be all possible distributions from $\mathcal{X}$ to $\mathcal{Y}$. 
How do I visualize this situation in terms of sets and geometry? I particularly cannot see $\mathcal{P}_{X|Y}$. I understand that that is a set of all possible distributions but how do I visualize it?
EDIT:
 I read some more about this, and I see that probability distributions depend on the measure employed, Lebesgue, $\mu$, for continuous and counting, #, for discrete. I still don't understand what are the various points will be for a distribution visualized as a set.
I ask this because there are extreme points defined for probability spaces, so I infer that they must be visualized as sets to do this.

Provided $n$ is size of $\mathcal{X}$ and $m$ is size of $\mathcal{Y}$, all possible joint probability distribution functions $\mathcal{P}_{X,Y}$ are $n+m$ dimensional vectors with non-negative components such that sum or first $n$ components and the other $m$ components have to be one. 
If $n=m=2$, then $\mathcal{P}_{X,Y}$ can be drawn as a square $[0,1]^2$ where the first component is the probability that $X=1$ and the second one that $Y=1$.
If we consider the conditional case, note that for each fixed $x\in\mathcal{X}$, the possible $\mathcal{Y}$ remains the same. Moreover, the set of all potential conditional probability distributions on $\mathcal{Y}$ are the same for any $x\in\mathcal{X}$. The set of all probability distributions on $\mathcal{Y}$ are non-negative real vectors of dimension $n$ having sum one. For $n=3$ this can be shown in $\mathbb{R}^3$ as triangle with vertices $(0,0,1)$, $(0,1,0)$, and $(1,0,0)$. This triangle is the same for any $x\in\mathcal{X}$.
