Mich. Comp. Laws § 168.444

Sec. 444. (1) If a vacancy occurs in the office of judge of probate, the governor shall appoint a successor to fill the vacancy. Except as otherwise provided in section 435a(2), the person appointed by the governor shall be considered an incumbent for purposes of this act and shall hold office until 12 noon of January 1 following the next general November election at which a successor is elected and qualified. (2) Except as otherwise provided in section 435(2), if the vacancy occurs more than 7 days before the nominating petition filing deadline as provided in section 433 for the general November election that is not the general November election at which a successor in office would be elected if there were no vacancy, the person appointed shall hold office only until a successor is elected at the next general November election in the manner provided for in this chapter for the election of judges of probate. The person elected shall hold office for the remainder of the unexpired term.