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When is it safe to cancel a term when marginalizing over a distribution (to reduce the bulk of computation)?

Consider the example:

p(a,b,c,d,e) = p(c|a,b)p(a)p(b)p(d|a)p(e|d,b)

suppose we would like to find p(e=1|b=1) = p(e=1,b=1) / p(b=1)

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