(a) On a petition for the probate of a will, if the court finds that the testator is dead, that the instrument offered for probate was executed in all respects according to law when the testator was competent to do so and acting without undue influence, fraud, or restraint, that the will was not revoked, and that the instrument is his or her last will, then the will shall be admitted to probate as the last will of the testator, but the order need not recite such findings.
(b) On the petition for the appointment of an executor or general administrator, the court shall determine whether the deceased died testate or intestate and shall grant letters accordingly or, on proper grounds, deny the petition.