The mathematics of uncertainty
Conditional distributions are conditional probability, lifted to whole random variables. Given that X = x, how is Y distributed? You take the joint and renormalize by the marginal of the thing you've fixed:
It's the same zoom-and-renormalize move from Lesson 3: fix X = x (pick one row of the joint table), then rescale that row so its probabilities sum to 1. The result is a genuine distribution over Y, one for each value of x.
Go back to the height–weight table, but now look at one single row — say, only the tall people — and ignore everyone else. That row's numbers don't add to 1 on their own, so you rescale them until they do, and what you get is how weight is distributed given that height is tall. That is a conditional distribution: fix X = x to one category, then renormalize that slice into a proper distribution over Y.