Conditional Probability Calculator
Enter the joint probability P(A∩B) and the probability of the condition P(B) to get P(A|B) — the chance of event A once event B is known.
Two inputs, one answer
Enter the joint probability P(A∩B) and the probability of B, and the calculator returns P(A|B) = P(A∩B) ÷ P(B) as a value between 0 and 1.
Use decimals 0–1
Both inputs are probabilities between 0 and 1, and P(B) must be above 0 — you cannot condition on an event that never happens.
What is conditional probability?
The chance of A once B is known
A conditional probability calculator answers a focused question: once you know that event B has happened, how likely is event A? Written P(A|B), the conditional probability rescales the joint probability P(A∩B) by the probability of the condition P(B). Knowing B has occurred narrows the world down to just the outcomes where B is true, and within that smaller world we ask what fraction also has A. The result is always a probability between 0 and 1, and it underpins everything from medical test interpretation to spam filters and risk models.
Enter the joint probability P(A∩B) and the probability of B to get the conditional probability P(A|B) instantly.
The conditional probability is the joint probability divided by the probability of the condition.
P(A|B) = P(A∩B) ÷ P(B)Because the joint event A∩B is always a subset of B, the numerator can never exceed the denominator, so the result stays between 0 and 1. Dividing by P(B) is exactly the step that restricts attention to the outcomes where B has occurred.
Suppose the joint probability of A and B is P(A∩B) = 0.2 and the probability of B is P(B) = 0.5.
Take the joint probability
P(A∩B) = 0.2 — the chance that A and B happen together.
Divide by P(B)
0.2 ÷ 0.5 — rescale by the probability of the condition B.
Read the result
P(A|B) = 0.4 — given that B occurred, there is a 40% chance of A.
The result is the probability of A within the world where B is already known to have happened. In the example, P(A|B) = 0.4 means that among all the times B occurs, A also occurs 40% of the time. Compare this against the plain probability of A: if P(A|B) equals P(A), then B tells you nothing new about A and the two events are independent. If the conditional probability is higher than P(A), then B makes A more likely; if it is lower, B makes A less likely. This single comparison — P(A|B) versus P(A) — is the heart of how conditioning changes belief, and it is why a positive medical test, a clicked link, or an observed symptom can shift the odds of an underlying event so sharply.
The formula is exact, but it needs the right inputs to mean anything.
You need the joint probability and a possible condition
This calculator uses the direct definition P(A|B) = P(A∩B) ÷ P(B), so it requires the joint probability P(A∩B), not just the separate chances of A and B. The condition must be possible — P(B) has to be greater than 0, because you cannot condition on an event that never happens. The joint probability also cannot exceed P(B), since A∩B is a subset of B. If you only know P(B|A), P(A), and P(B), reverse the conditional with Bayes' theorem instead.