Respuesta
$P(A|B) = \frac{\text{Number in category } A \text{ and } B}{\text{Total in condition category } B}$. Restrict your denominator strictly to the given condition group, not the grand total.
Explicación
Phrases like 'Given that the person is in group B...' or 'Of those who tested positive...' signal that the total sample space is restricted to group B.