(a) The county clerk has the duty to record in well-bound books all letters testamentary and of administration, all guardian appointments and all settlements made by the clerk with guardians and personal representatives.
(b) Subsection (a) shall only apply in counties having a population, according to the 2000 federal census or any subsequent federal census, of:
(c) In counties having a population of not less than thirty-nine thousand fifty (39,050) nor more than thirty-nine thousand one hundred fifty (39,150), according to the 2000 federal census or any subsequent federal census, the circuit court clerk, who also serves as the general sessions court clerk, shall serve as the clerk of the court with probate jurisdiction in any such counties.