 where \(\Pr'(X_k = x_k) = 1\). The conditional probabilities of the form \(\Pr(X_i \mid \bPA(X_i))\) for \(i \ne k\) remain unchanged by the intervention. This gives the same result as computing the result of an intervention using a SEM, when the latter is available. This result can be generalized to the case where the intervention imposes a probability distribution \(\Pr^{\dagger}\) on some subset of the variables in \(\bV\). For simplicity, let’s re-label the variables so that \(\{X_1, X_2 ,\ldots ,X_k\}\) is the set of variables that we intervene on. Then, the post-intervention probability distribution is: