Computing conditional probability combining events I know $P(E|A)$ and $P(E|B)$, how do I know $P(E|A,B)$? Assuming $A,B$ independent.

Consider this example: 


*

*$A$ = first coin lands Head, 

*$B$ = second coin lands Head, 

*$E_1$ = odd number of Heads, 

*$E_2$ = even number of Heads. 


The first two conditional probabilities are both $1/2$. The third is $0$ for $E_1$ and $1$ for $E_2$.
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