Stanford Encyclopedia of Philosophy
Supplement to Inductive Logic
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Immediate Consequences of the Independent Evidence Conditions

When neither independence condition holds, we at least have: 

P[en | hj·b·cn]	=	P[en | hj·b·cn·en−1] · P[en−1 | hj·b·cn]
	=	…
	=	n Π k=1 P[ek | hj·b·cn·e k−1]

When condition-independence holds we have:

P[en | hj·b·cn]	=	P[en | hj·b·cn·(cn−1·en−1)] · P[en−1 | hj·b·cn·cn−1]
	=	P[en | hj·b·c n·(cn−1·en−1)] · P[en−1 | hj·b·cn−1]
	=	…
	=	n Π k=1 P[ek | hj·b·ck·(ck−1·ek−1)]

If we add result-independence to condition-independence, the occurrences of ‘(c^k−1·e^k−1)’ may be removed from the previous formula, giving:

P[en | hj·b·cn]

=

n Π k=1

P[ek | hj·b·ck]

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Supplement to Inductive Logic
Stanford Encyclopedia of Philosophy