Bicyclists who test actual positive (who actually use steroids) = 0.08 * 0.96 = 0.0768

Now, bicyclists who test false positive (i.e. the ones who do not use steroids but still test positive) = 0.92 * 0.09 = 0.0819

$\therefore$ Total bicyclists who test positive = 0.0768 + 0.0828 = 0.1596

Favorable cases (the ones who actually use steroids) = 0.0768

So, required probability = $\frac{0.0768}{0.1596}$ = 0.4812 = 48.12%