A Chelsea man’s conviction of possession of PCP was reinstated Tuesday by the state Supreme Judicial Court, according to the Suffolk district attorney’s office. Tim Cullity, 59, was found guilty in Chelsea District Court on Nov. 16, 2011, after a police officer found the hallucinogenic drugs during a motor vehicle stop a year earlier, the district attorney’s office said in a statement. The Massachusetts Appeals Court overturned the decision in 2014 on grounds that the evidence in the lower court was insufficient. But the SJC disagreed and reinstated the conviction. Cullity will not have to serve jail time after completing a probationary period of one year.