You cannot move to a different county unless your probation officer okays it or unless it is specifically allowed by the written terms of your probation. Being on probation means you do not have the same freedom as everyone else.
This is not legal advice. This is only intended for public informational purposes. Legal advice can only be given in a confidential setting with a lawyer. Websites like this are useful, but contain inherent limitations. Keep in mind that laws differ from state to state. If you have a criminal charge, you should consult with a local lawyer in your community for confidential legal advice.