Probability issue given a Bayesian Network

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If we have a Bayesian Network A -> B ->C then P(B|A, C) = P(B|A)?

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$P(B|A,C)=\dfrac{P(A,B,C)}{P(A,B,C)+P(A,\text{not }B,C)}=\dfrac{P(B|A)P(C|B)}{P(B|A)P(C|B)+P(\text{not }B|A)P(C|\text{not }B)}$