Draft up a heartfelt letter of explanation. Explain exactly what happened, what the circumstances around the incident, how the person has not had any other issues since then, is no longer on probation, and why that type of incident won't happen again.
You may have to offer a larger security deposit or add a little bit extra to the monthly rent. You can also get referrals from your previous landlords and ask them to write a letter for you along with their contact information saying that you were an outstanding tenant, etc.
Give them this letter when you submit your application so that they are not surprised when they pull the credit report and background check. This will show that that you are not trying to hide anything.
I wish you the best of luck in your situation. I know it can be difficult.
B&B Realty Group - Keller Williams Elite Dallas TX