Random testing means just that. Probation has the right to come to your home and test you for alcohol. They can show up at anytime. Besides being tested when you appear once a month. This is the law in NY...I don't really know in Utah.
Your best bet would be to get into recovery. If your drinking...you will eventually get caught. Your playing Russian Roulette IMO. If you test positive, you WILL be arrested on the spot!
Best Wishes To You!