Total number of ways in which any 3 random people can be chosen from 100 is $\binom{100}{3}$.
Now in our favourable cases, Michelle wins the prize, so in all favourable cases, Mitchelle is one of the 3 persons in the set which is chosen for winning. Now other 2 persons can be chosen in $\binom{99}{2}$ ways, so probability is
$P = \frac{\binom{99}{2}}{\binom{100}{3}} = \frac{\frac{99*98}{2}}{\frac{100*99*98}{6}} = 0.03$