Bayes Law formula query

What I don’t get is how the formula is:

(Probability of new information / Unconditional Probability of New Information) * Prior Probability of Event

However, whenever it is applied in an example or question we do this:

(Conditional probability of event / Unconditional Probability of Event)

Where are the probabilities of the new information and why aren’t we multiplying by the prior probability of the event.

I’m not sure I understand your question but let’s just define Bayes’ Theorem:

P(A|B) = \frac{P(B|A)}{P(B)}{P(A)}

Where P(A\cap{B}) = {P(A|B)}\times{P(B)} = {P(B|A)}\times{P(A)}

Therefore,

P(A|B) = \frac{P(A\cap{B})}{P(B)}

Where {P(A\cap{B})} is the probability of both A and B occuring.

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