There is a medical examination to see if you have a disease. The test result is P(Test | Disease), which is forward probability. But people are more interested in the inverse probability, P(Disease | Test).

P(D | T) may not be the same for different types of patients because patients with a family history of the disease should get more attention if they get a positive test than if they don't have a family history of the disease.

$P(D | T) = likelihood\ ratio * prior\ probability\ of\ D$ $Likelihood\ ratio = P(T | D) / P(T)$ where, P(T|D) is the sensitivity of the test technique.

Take Away: The forward probability P(T | D) is completely insensitive to many individual factors of the patient because the forward probability is more dependent on the test technology itself, while the backward probability P(D | T) is very sensitive to factors affecting the prior probability such as the patient's living habits, living environment, economic status, family history, etc.