Discuss the below:
A rare disease has just broken out. Doctor Johnson is trying to help, but while treating patients he might expose himself to the disease. He takes many precautions, but he doesn't know how much he's been exposed. Let the number x represent Doctor Johnson's exposure level. He doesn't know it for sure, but he assigns a uniform distribution to it(between 0 and 1). He also assigns a probability
{Doctor Johnson gets disease | x} = x^2
Doctor Johnson has just come down with the disease. What is his new distribution for his exposure level?