Say the number of people infected is x. Then 98% of them will test positive, so 0.98x.

Say the number of people not infected is y. Then 3% of them will test positive (falsely), so 0.03y.

There is no guarantee that together you get the total number of people who are infected. It's just saying that of those infected, 98% will show up positive on the test, and from those not infected, 3% will receive a false positive.

Now your question is asking "If a person selected at random responds positively to the test, what is the probability that the person actually has the disease?"

Another way of saying this is "What is the probability of a person actually having the disease given that the person tested positive?"

This is a conditional probability, so you need to use the conditional probability formula.