(a) The probate court shall have exclusive jurisdiction over the probate of wills.

(b) The county of domicile of the testator at death shall give jurisdiction to the probate court of that county.

(c) The domicile of a testator who was in the care of a nursing home or other similar facility at the time of death shall be presumed to be the county in which the testator was domiciled immediately before entering the nursing home or other facility; provided, however, this presumption may be rebutted. If it is determined by the probate court that the testator considered or, in the absence of an impairment of mental faculties, the testator would have considered the county in which the facility is located to be the testator's domicile, then for purposes of this Code section that county shall be considered the testator's county of domicile.