If the agreement was that the charge would be dismissed upon your successful completion of probation, and you successfully completed probation, you shouldn't have a conviction. In a small number of cases there is a mistake by the court and the record is incorrect, so you may wish to verify that your record is correct. A full background check may also show any arrest, and the original charge, as well as the disposition (while reflecting that it was not a conviction) - that will vary by state.

