linguistic:translation
For events

The events A {\displaystyle A} and B {\displaystyle B} are conditionally independent given an event C {\displaystyle C} when

P (A ∩ B ∣ C) = P (A ∣ C) ⋅ P (B ∣ C) {\displaystyle \mathrm {P} (A\cap B\mid C)=\mathrm {P} (A\mid C)\cdot \mathrm {P} (B\mid C)}.