Create a Predictive model to find users that would book an exam
Your problem is a kind of Binary Classification which predicts the probability of a target variable to be Yes(1) or No(0).
But, first of all, you need some ground-truth data, because most of the state-of-the-art solutions to this problem are supervised.

If you're the admin of this system or have access to their server, you can collect these data by logging everything you need from every user and label their traces with 1 and 0 when they book or not.

After a while, you have a big labeled dataset and you can normalize and shape your inputs in a way that it fits for example to a deep neural network for prediction.