Yes. And, yes.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
The police can run your name and find out that you are on probation. Depending on the nature of the run in, the police may or may not tell your PO. If you were charged with a crime, expect your PO to find out about it. Even if you were not charged with a crime, your conduct may still be a violation of your probation. What you don't want to do is volunteer the information to the PO. Good luck.