Basically a conditional distribution is some subset of the exhaustible distribution.
So as an example, a common distribution looks something like P(Y|X=x). So if you only have a joint distribution with Y and X as random variables, then typically what happens is you are selecting a "slice" distribution for some fixed X=x.
Basically all your are doing is your selecting a subset of the probability distribution space and nothing more. You can make it more complicated if you want to (like say P(Y|X<2) or P(Y|X is an integer) but it's always the same basic concept.