(a) Whenever a vacancy, either by death, resignation or removal, occurs in the office of county judge, it shall be filled by the qualified voters of the county at the first regular election in August for any of the county officers, more than forty-five (45) days after the happening of the vacancy. In the meantime, the county legislative body, at its first meeting after the happening of the vacancy, shall elect a person learned in the law and legally qualified to discharge the duties of the office until the election by the people can be had. If the county legislative body fails or refuses to elect a successor to fill the office until the next regular August election, at its first meeting after the happening of the vacancy, then the governor shall appoint some person learned in the law and legally qualified to discharge the duties of the office, who shall serve until the next regular election in August, at which time the vacancy shall be filled by the qualified voters of the county.

(b) Unless the county legislative body is to have a regular meeting within ten (10) days after the vacancy occurs, it shall be the duty of the county clerk, or, in the county clerk's absence or inability to act, of the county clerk's deputy, and the clerk or deputy is empowered, immediately upon the occurrence of the vacancy, to give notice of a special meeting of the county legislative body to be held ten (10) days after the date of the notice, unless the date thus set falls upon a Sunday or holiday, in which case the meeting shall be fixed for the next business day, for the election of the person to fill the vacancy. The meeting shall be held upon the date thus fixed, and the presiding officer for the meeting shall be elected by the county legislative body.