“The car in front of me just swerved halfway into my lane. How likely is the driver to be drunk?"
These underspecified problems are the meat of day-to-day probability judgments.
Well, it is not beyond the realm of possibility that the boy could have stabbed his father and disposed of the knife altogether, so even if he is guilty, there is no guarantee of seeing the knife. However, since we know he did buy an identical knife, it is not very surprising to see it at the crime scene if he is guilty. Let us estimate this probability as P(knife|guilty) = 0.6.
The base rate for bowel cancer looks to be about 54 per 100,000 or around 2000:1 against, so O(cancer|pos_test) = (1:2000)*10 = 1:200 in favor = 200:1 against. As you can see, a positive test is cause for concern, but not panic. You probably don’t have the disease. In fact, you didn’t even need to look up the incidence in this case - all you needed to do was realize that unless 1 in 10 people in your reference class have bowel cancer (surely not!), your odds of having it are less than 50:50.