The page on conditional probability calculates probabilities of drawing the short match. Among other things, there are several fraction divisions that go like this:
1/5 / 5/6 = 1/6
and
1/4 / 4/6 = 1/6

Though the outcomes seem to agree with the meaning of the probabilities calculated, the arithmetic does not.

Any thoughts?

http://www.cut-the-knot.org/Probability/ConditionalProbability.shtml