Just in case a picture helps...
... with W = well, I = ill, P = testing positive, N = testing negative...
See here Conditional probability - Wikipedia, the free encyclopedia for a more formal treatment of a very similar problem (see under the heading 'An example'), but from the tree you can see that
(b) is (398 + 99) / 20,000
and (c) is 99 / (398 + 99)
(a) is disconcertingly more obvious and (if I'm not mis-reading it) just 98%. Hope this helps.
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!