The probability that, if I get caught by a red light at one set of traffic lights, I will get a green at the next lights is an example.
May - or may not - be a conditional probability. A conditional probability is not becessarily chronologically structured.
It can be called a "conditional probability", but the word "conditional" is irrelevant if the two events are independent.
Conditional probabilities arise when you revise the probabilities previously attached to some events in order to take new information into account. The revised probabilities are 'conditional on the new information you have received'.
If events A and B are statistically indepnedent, then the conditional probability of A, given that B has occurred is the same as the unconditional probability of A. In symbolic terms, Prob(A|B) = Prob(A).
The probability of event A occurring given event B has occurred is an example of conditional probability.
Tree diagram
A conditional event.
The conditional probability is 1/4.
This is a conditional probability, given the card is red, what is the chance it is a heart. Since there are 2 red hearts, the probability if 1/2
If the events are independent then you can multiply the individual probabilities. But if they are not, you have to use conditional probabilities.
Probability of getting a King is 4/52 = 1/13. Having drawn the King, for it to be a Red King, the probability is 2/4 = 1/2. Hence the conditional probability is (1/13)x(1/2) = 1/26
It is the integral (or sum) of the joint probability distribution function of the two events, integrated over the domain in which the condition is met.