 and a probability distribution \(\Pr'\) on the exogenous variables \(\bU\). \(\Pr'\) then induces a probability distribution P on \(\bV\). To represent an intervention that sets \(X_k\) to \(x_k\), we replace the equation for \(X_k\) with \(X_k = x_k\). Now \(\Pr'\) induces a new probability distribution P* on \(\bV\) (since settings of the exogenous variables \(\bU\) give rise to different values of the variables in \(\bV\) after the intervention). P* is the new probability distribution that Pearl writes as \(\Pr(• \mid \ido(X_k = x_k))\).