I am having hard time interpreting the relationship, if any, between conditional probabilities vs. conditional probability distributions, in particular, regarding the number of random variables required to be able to define these two concepts.
As I understand, conditional probability can be defined for events involving a single random variable. For example, we could ask what is the probability that a die roll resulted in 4 given that the number is larger than 3, i.e., $P(X=4 | X>3)$.
However, the conditional probability distribution is based on the concept of joint distribution, which requires two or more random variables.
My question is whether it makes sense to talk about the conditional probability distribution of a single random variable or, conversely, whether a conditional probability statement like the one above can be related to a conditional probability distribution?