Can conditional probability P(A|C) be expressed as a sum over P(A|B)P(B|C)?

[ravi.xolve]

Consider the conditional probability P(A|C) .

Is it true that we can calculate above as

Summation over B P(A|B)*P(B|C) .

 

[lanedance]

You'll need some conditions on the Bi for that to be true