Conditional Independence and d separation

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I am reading Pattern Recognition and Machine Learning by Christopher M. Bishop. I am unable to proof one of the steps. The question is of Bayesian Belief networks: Head to Tail Case

3 node graph to show conditional independence $$ P(a,b,c) = P(a) * P (c|a)* P(b|c) $$

Suppose that none of the variables are observed. We can test to see if a and b are independent by marginalizing over c to give

$$ P(a,b) = P(a) * \sum_{c} P(c|a)* P(b|c) $$

Now the next step which I am unable to understand how it got here:

$$ P(a,b) = P(a) * P(b|a) $$