(a) After a legal service provider has rendered services, or failed to render services, to a client out of which a claim has arisen, the parties thereto may agree to settle such dispute by arbitration. Such agreement must be in writing and signed by both parties. Any such agreement shall be valid, binding, irrevocable, and enforceable, save upon such grounds as exist in law or in equity for the revocation of any contract.
(b) Pursuant to the provisions of this section, the claimant shall select one competent and disinterested arbitrator, and the party or parties against whom the claim is made shall select one competent and disinterested arbitrator. The two arbitrators so named shall select a third arbitrator, or, if unable to agree thereon within 30 days, then upon request of any party, such third arbitrator shall be selected by a judge of a court of record in the county in which the arbitration is pending. The arbitrators shall then hear and determine the question or questions so in dispute in accordance with the procedural rules established by the American Arbitration Association. The decision in writing of any two arbitrators shall be binding upon all parties. Each party shall pay fees of his own arbitrator, and split the expenses of the third. Arbitration shall be conducted in the county in which the claim arose. A judgment upon the award rendered by the arbitrators may be entered in any court having jurisdiction thereof.