Graphical separation in a causal model indicates that there is conditional independence in the data.
$$(X sep Y|Z)_{G(M)} \Rightarrow (X \bot Y|Z)_{P(v)}$$

University of Michigan - Ann Arbor

This implies that given a system where only three events A, B and C, occur, 

$$P(A, B| C) = P(A|C) . P(B|C)$$

That is, knowing the value of C does not help us better ascertain the values of A and B.

Conditional Independence

1. The Law of Counterfactuals
2. The Law of Conditional Independence

The Two Fundamental Laws of Causal Inference

https://www.youtube.com/watch?v=ZaPV1OSEpHw&t=1419s

Judea Pearl Lecture

The Law of Conditional Independence

If there is a model of the universe that perfectly maps how a variable effects and is effected by its neighbors you can generate all possible counterfactuals. Under this model a counterfactual can always be represented by this equation. $$Y_x(u)$$ is the event if it were to have occured and $$Y_{M_x}(u)$$ is the event as a counterfactual.

$$Y_x(u) = Y_{M_x}(u)$$

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