In many states, apparently including Florida, probate court is "family court". Probate judges handle wills and estates, but also the appointment of guardians for orphans, the legal changing of names, and other such personal legal matters. That is why, quite logically, the Florida legislature gave Florida probate courts jurisdiction over adjudging someone in a PVS - because probate courts handle other kinds of guardianships as well.
I well understand the supposed "logic" behind it, I am a paralegal.