(a) Unless otherwise provided by local law, the governing authority of the county shall determine whether the prosecuting attorney of a probate court shall be a full-time or part-time prosecuting attorney.
(b) Any full-time prosecuting attorney of a probate court and any full-time employees of the prosecuting attorney of a probate court shall not engage in the private practice of law.
(c) Any part-time prosecuting attorney of a probate court and any part-time assistant prosecuting attorney of a probate court may engage in the private practice of law, but shall not practice in the probate court or appear in any matter in which that prosecuting attorney has exercised jurisdiction. A prosecuting attorney of a probate court and any assistant prosecuting attorney of a probate court shall be subject to all laws and rules governing the conduct of prosecuting attorneys in this state.