How can this expression be derived?
p(a,b|c) = p(a|b,c).p(b|c)
where a,b,c are random variables.
UPDATE: from the following video lecture: Graphical Models 2- Christopher Bishop. ( http://www.youtube.com/watch?v=c0AWH5UFyOk ) skip to 3 min 11sec
Hint: Use the following facts:
(1)$P(A\cap B|C)=\frac{P(A\cap B\cap C)}{P(C)}$
(2)$P(A\cap B\cap C)=P(A|B\cap C)P(B\cap C)$