Totally not a statistician, but I'll give it a shot.

For the sake of the argument:

  test accuracy: exactly 99.0% accurate
  disease incidence: exactly 1 in 1 million

Calculation:

  For the sake of simple calculations, let's assume we test exactly 1 million people.

  tests positive = (1 * 0.99) + (999999 * 0.01)
  tests positive = (.99) + (9999.99)
  tests positive = 10000.98

We'll round up for the sake of argument to 10,001 positive results. And we know that only 1 person (remember that we're testing 1 million people) is actually sick. We have 1 actual sick in 10 thousand positives tests. So the probability that the positive test that is right in front of you is actually a truly sick person are 1 in 10 thousand.