Implement Bayes' Theorem

You work for an insurance company. An analyst comes into your office in a panic. They have been asked to implement AI in a new proof of concept and need to use Bayes' Theorem to help predict the results of someone having a life-threatening disease.

Help the analyst out. How would you explain Bayes' Theorem to them? How would you connect it to the way insurance companies assess risk, and to this problem in particular?