(a)   A taxicab driver's license may be denied to any applicant who, within ten years prior to the application, has been convicted of an offense under Federal, state or local law, whether charged under such statutes or a local ordinance.
   (b)   The license shall be denied in the event of a conviction of the applicant within such period of any offense involving gambling, illegal traffic in intoxicating liquor or in narcotics or against public morals herein.