Unfortunately the Judge will likely not answer your letter. There are formal ways to get things done in the court system, and many times the court staff screens out letters that would otherwise go to the Judge. The reason, again, is due to the requirement for formal procedure.
It is possible to request early release from probation, without going through your case and learning more about the situation that you are in, I would be unable to tell you what your chances are.
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Sometimes a motion for early termination of probation may be granted, especially if the request is supported by the supervising probation officer and two-thirds or so of the probationary period has passed and all conditions have been met.
I believe that you or your lawyer would need to make such a motion, possibly with supporting affidavits and memorada of law, and schedule a hearing. I do not beleive a court could grant the requested relief ex parte (without an opportunity for the prosecutor and court services to be heard on the request) - just on a letter or any written request alone. I bleive the judge would need to set a hearing, with notice to all concerned.