(1) All of the following apply in a contested case:

    (a) A petitioner who seeks to establish intestacy has the burden of establishing prima facie proof of death, venue, and heirship.

    (b) A proponent of a will has the burden of establishing prima facie proof of due execution in all cases and, if the proponent is also a petitioner, prima facie proof of death and venue.

    (c) A contestant of a will has the burden of establishing lack of testamentary intent or capacity, undue influence, fraud, duress, mistake, or revocation.

    (d) A party has the ultimate burden of persuasion as to a matter with respect to which the party has the initial burden of proof.

    (2) If a will is opposed by a petition for probate of a later will revoking the former, the court shall first determine whether the later will is entitled to probate. If a will is opposed by a petition for a declaration of intestacy, the court shall first determine whether the will is entitled to probate.