If a couple has three daughters what is the probability that the next child is a son if they already have three daughters?

There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes.
If you believe that the children's genders are not independent then you would need to get empirical evidence from all families with four or more children in which the first three children were girls. If there are g families in which the fourth is a girl and b where the fourth is a boy then the required probability is b/(g+b).

However, if you assume that the children's genders are independent events then, given that the probability of a boy is approx 0.52, the probability of the fourth child is a boy is 0.52