How to calculate $P(A, B | C)$ from Bayesian Network? I have this bayesian network: 
A -> B -> C I need to calculate $P(A, B|C)$. How can I do that? 
I tried doing:
$P(A,B | C) = P(A|B,C)P(B|C)$
But I don't understand where to go from that considering I don't have any CPT that can help me in solving $P(A|B,C)$. I only have CPT's where $B$ is dependent on $A$ and $C$ is dependent on $B$. 
Also, what should I read to be able to solve such weird flows' probabilities in the BN?
 A: In your network, the CPDs are P(A), P(B|A) and P(C|B). Also, C is independent of A given B. 
$$
\begin{align}
P(AB|C)&=P(C|AB)P(AB)/P(C) \\
&=P(C|B)P(B|A)P(A)/(\sum_B P(C|B) \sum_A P(A)P(B|A))
\end{align}
$$
P(C) is calculated by summing out A and B from the joined distribution.
It's not a "weird" form, instead rather basic. You can read about conditional independence and information pass in the field of graphical models to learn more about it.
A: note1: you also have the probability table for $A$. You can think of it as the CPT for $P(A|\phi)$.
note2: at least when beginning with bayesian networks, I think it helps a lot to use the full notation $P(B=b|A=a)$, to understand what you're doing. Think of $A$ as a binary random variable that can take $a \in [0,1]$ 
If the network was only A->B, to derive $P(B=b|A=a)$, you would do:
$P(A=a, B=b) = P(A=a)P(B=b|A=a)$
$P(B=b) = \sum_{a\in A}P(A=a)P(B=b|A=a)$
so:
$P(A=a|B=b) = \frac{P(A=a,B=b)}{P(B=b)}$
for 3 variables, just apply these Bayesian equations more. 
