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We have the following relationship, and you have all you havethe things in the numerator part ready: $$P(B|C,A)=\frac{P(A|B,C)P(B|C)}{P(A|C)}$$
But, you don't know $P(A|C)$ or anything else that will help you to calculate it.
We have the following relationship, and you have all you have the numerator part ready: $$P(B|C,A)=\frac{P(A|B,C)P(B|C)}{P(A|C)}$$
We have the following relationship, and you have all the things in the numerator part: $$P(B|C,A)=\frac{P(A|B,C)P(B|C)}{P(A|C)}$$
