(a) $P(\text{Abby winning first prize}) = \frac{1}{200}$
$P(\text{Barry winning second prize}) = \frac{1}{199}$, as Abby can't win more than one prize.
$P(\text{Sylvia winning third prize}) = \frac{1}{198}$
So total probability = $\frac{1}{200}*\frac{1}{199}*\frac{1}{198}$
(b) Now total probability = $\frac{1}{200}*\frac{1}{200}*\frac{1}{200}$, because everyone can win any number of prizes.