How to introduce time parameter in an equation?

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I was working for my project. And in my project I need to use conditional probability. Actually I need to find probability of an event A, given that event B already occurred ahead of time

Say A is an event which is electricity blackout and B is an event which is high heatwaves. Now, I want to find out P(electricity = blackout | heatwave = high). I can find probability by using Bayes' theorem. But, If I want to find probability ahead of some 'X' time. Then what should I suppose to do?

I have little knowledge on math tools. Like I was thinking does derivative do anything here to bring time in account? How actually researchers say somethings like probability of rising global temperature within 5 years given that if we cut down forest by x%?

I also got confused on what different context do I need to use conditional probability and bayes' theorem?