(a) Whenever an election fails to fill the office of county surveyor, the judge of the probate court shall appoint a person to serve as the county surveyor until a successor is duly elected in a special election which shall be held at the time of the next general election to serve out the remainder of the unexpired term of office.

(b) In the event that a vacancy occurs in the office of county surveyor, the judge of the probate court shall appoint a person to serve for the unexpired term of office and until his successor is duly elected and has qualified.