If you plead no contest for a Misdemeanor B and are serving probation were you convicted of the crime?

Pleading "nolo contende" to anything signifies that you chose not to contest the charges are filed. For all intents and purposes, that's just as good as pleading guilty but without the soul cleansing honesty.

And yea, for probation purposes it is as good as committing another offense. Whether or not the P.O. chooses to violate the offender will depend on what exactly the offense was.