GIVEN
P(A|B) = "Probability of A, given B happened"
P(A|B) = P(A∩B) / P(B)
SHRINK
Conditioning shrinks the sample space to B only
New universe = B
CHAIN
Multiply along the tree: P(A∩B) = P(A)·P(B|A)
P(A∩B) = P(B)·P(A|B)
BAYES
Flip the conditional — prior × likelihood ÷ evidence
P(A|B)=P(B|A)·P(A)/P(B)
INDEP
Independent ⟺ knowing B changes nothing about A
P(A|B) = P(A)