The first P term is the outcome of the Daisy experiment. It represents the probability of successful house training ($Y = 1$), given that we set X to 0 (do not introduce other pets) but set the mediator $M$ to $M_1$ (the value it would have if we had introduced them). The counterfactual $M_1$ needs to be computed accordingly: different dogs might have different needs for supervision. The second P term is the probability of successful house training of the dog under the condition with no other pets. Here we set $X = 0$ to reflect that no other pets are present, and $M = M_0$ to reflect that we do not introduce the mediator.