Newborn's sex after a boy is picked from the nursery

A nursery contains $3$ boys and some unknown number of girls. A newborn, equally likely to be a boy or a girl, is added. A nurse then picks a child at random from the nursery and it is a boy. What is the probability that the newborn is a boy?

$4/7$. With $g$ girls, a boy is picked with probability $\tfrac{4}{g+4}$ if the newborn is a boy and $\tfrac{3}{g+4}$ if not. The common denominator and equal priors cancel in Bayes' rule, leaving $\tfrac{4}{4+3}=\tfrac47$ regardless of $g$.