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What is the difference between conditional probability and distributed multiplication and counting principle in high school mathematics?
Conditional probability is simply to give the situation of an event, and then let you find the probability of this event.

A simple example is: in coin toss, assuming that the coin is even and tossed twice, we know that the probability of a coin is 1/2 without giving conditions, but we give a condition (a coin is known to be upside down), so the probability of asking a coin to be upside down is called conditional probability, which is 2/3.

The principle of step-by-step multiplication is a mixture of multiplication principle and addition principle.