 We have a probability distribution \(\Pr'\) on \(\bU\), which induces a probability distribution P on \(\bU \cup \bV\). Suppose that we observe the value of some of the variables: \(X_j = x_j\) for all \(j \in \bS \subseteq \{1,\ldots ,n\}\). We now want to assess the counterfactual “if \(X_k\) had been \(x_k\), then \(X_l\) would have been \(x_l\)”, where k and l may be in \(\bS\) but need not be. We can evaluate the probability of this counterfactual using this three-step process: