# Ad classification problem, several binary vs. one multiclass model

I have a website that shows 3 ad panels at a time. These ads can belong to three different classes (each ad can only belong to a single class, there is not multilabeling).

I want to build a model that gives me the probability of a user clicking (or not clicking) on the ad under the condition that the ad belongs to a particular class. In other words I want $$P(click|C=1)$$, $$P(click|C=2)$$ and $$P(click|C=3)$$.

Now, my first thought was to build one binary classifier for each one of these classes, using only the data relevant to each class at a time.

Someone told me I could probably use a multiclass classifier to do this (in particular, a multilayer perceptron). I think this will not work, since a multiclass classifier will have to learn how to predict the probability that the ad is of a given class AND if it was clicked on (a total of six classes).

My questions are:

1 - Does my argument make sense? I don't feel like it is convincing, can anyone help me put it in more precise (mathematical) terms?

2 - More importantly, is there a way to build a single model that will accomplish the task (instead of building three), as this person suggested?

Thank you.