When the defendant pleads guilty, or is convicted either by the court or by a jury, the court must render judgment thereon of fine or imprisonment, or both, as the case may be: provided, however, it appearing to the court that it is a proper case, the court may, in its discretion, suspend the execution of judgment, and at such time, or any time during the period of sentence in a county jail, may put the defendant on probation on such terms and for such time as it may prescribe. The period of probation ordered by the court under this section under a conviction or plea of guilty for a misdemeanor, indictable or otherwise, may be for a period of not more than two (2) years; provided that the court may extend the period of probation to include the period of time during which the defendant is a participant in a problem solving court program and for a period of up to one (1) year after a defendant’s graduation or termination from a problem solving court program. The court may withhold judgment on such terms and conditions as it deems necessary or expedient.