Understanding predict_proba from MultiOutputClassifier
Assuming your target is (0,1), then the classifier would output a probability matrix of dimension (N,2). 
The first index refers to the probability that the data belong to class 0, and the second  refers to the probability that the data belong to class 1. 

These two would sum to 1.

You can then output the result by:

probability_class_1 = model.predict_proba(X)[:, 1]


If you have k classes, the output would be (N,k), you would have to specify the probability of which class you want.