Propensity model with Only Positive Data

Is it possible to build a propensity model (i.e., the likelihood that a user will buy an item) using only positive values.

For example, I have a bunch of data about Customers (people that bought stuff) and Users (people that haven’t bought stuff yet)
I want to get the likelihood that a User becomes a Customer.

It seems that the only way to do so is to train a model using the data of Customers, therefore using only Positive values.