An executor, administrator or surety on the bond of the executor or administrator of said estate, or the heirs or next of kin of such executor, administrator or surety may file a petition or complaint, verified by affidavits, in the court in which such a cause is pending, alleging the existence of the facts that raise the presumptions stated in section 43-2-660, and, upon the filing of such petition or complaint and giving security for costs of the proceeding, the court must appoint a day for the hearing of such petition or complaint and must give notice of the same by publication in some newspaper published in the county for three successive weeks or, if none is published in the county, by posting such notice at the courthouse and three other public places in such county for the same length of time; and the court must also give 10 days’ notice to every adult distributee resident in the state and to all sureties on the bond of the administrator or executor in said cause, of the day set for hearing the petition or complaint.