Upon petition by the governing body of any municipal corporation formed for local government, or of any county, and by vote of two-thirds of all the members of each house, the Legislature may pass private, special or local laws regulating the internal affairs of the municipality or county. The petition shall be authorized in a manner to be prescribed by general law and shall specify the general nature of the law sought to be passed. Such law shall become operative only if it is adopted by ordinance of the governing body of the municipality or county or by vote of the legally qualified voters thereof. The Legislature shall prescribe in such law or by general law the method of adopting such law, and the manner in which the ordinance of adoption may be enacted or the vote taken, as the case may be.