Pet shops are unlikely to prevail in a lawsuit accusing the state of Illinois of violating the equal protection clause by barring them from selling dogs or cats obtained from high-volume breeders, a federal judge held.In a written opinion, U.S. District Judge Iain D. Johnston of the Northern District of Illinois denied a motion by a group of pet shops to enjoin the enforcement of the state’s so-called “puppy mill” law.Puppy mills are commercial breeding facilities that engage in unethical or inhumane …