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