What would happen after being arrested for drunk in public while on probation for a DUI?

You should hire a lawyer and get this relatively minor charge dismissed and your DUI probation reinstated. By yourself you're going to get a new criminal charge and be found in violation of probation, and it isn't worth it.

Your probation officer will find out about it and it will be considered a violation of your probation. The prosecutor will file a motion to revoke your probation, there will be a hearing before a judge, and the judge may decide to revoke your probation and sentence you for the maximum penalty for your original DUI offense. I highly recommend that you report this violation to your probation officer and hire a lawyer to represent you at your probation revocation hearing.

Since you violated the terms of your sentence, there will be a hearing to discuss the infraction. You could get jail time, community service, pay a fine or all of these. With each violation, the sentencing terms get harder.