conditional probability

Is there a formula for conditional probability?
This probability is written P(BA), notation for the probability of B given A.
In the case where events A and B are independent (where event A has no effect on the probability of event B), the conditional probability of event B given event A is simply the probability of event B, that is P(B).
P(A and B) = P(A)P(BA).
What is conditional probability with example?
For example, if a person has dengue fever, the person might have a 90% chance of being tested as positive for the disease.
In this case, what is being measured is that if event B (having dengue) has occurred, the probability of A (tested as positive) given that B occurred is 90%, simply writing P(AB) = 90%.
What does PA ∩ B ') mean?
P(A ∩ B) indicates the probability of A and B, or, the probability of A intersection B means the likelihood of two events simultaneously, i.e. the probability of happening two events at the same time.
There exist different formulas based on the events given, whether they are dependent events or independent events.
We apply P(A ∩ B) formula to calculate the probability of two independent events A and B occurring together.
It is given as, P(A∩B) = P(A) × P(B), where, P(A) is Probability of an event “A” and P(B) = Probability of an event “B”.

Conditional probability refers to the chances that some outcome occurs given that another event has also occurred. It is often stated as the probability of B given A and is written as P(B|A), where the probability of B depends on that of A happening.

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