Whenever all the other conditions prescribed by section 39-1713 are present and, instead of being entirely shut off from all public roads, the only access by any owner of real estate to any public road is by an established private road less than two rods in width, the county board shall, upon the filing of an affidavit or affidavit and petition asking that an access road be provided in accordance with section 39-1716, substantially in the manner set forth in section 39-1713, setting forth such facts, appoint a time and place and hold a hearing thereon in the manner set forth in section 39-1713.