Find a conditional probability of a Bayes' Net knowing only the prior probability of the root.

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Given three nodes A,B,C that form a Bayes Network as the following:

(A)-->(B)-->(C)

If we know the prior probability of A is 0.3, i.e. P(A)=0.3, is this enough (and also reasonable) to start finding P(C|B), P(C|-B) and P(B|A), P(B|-A)? If not, does it mean that we should first know that probability distribution (e.g. uniform distribution) of all three nodes, P(A),P(B),P(C), before starting to calculate the conditional probability of this example?