OK, so to be eligible to become a United States citizen, you must meet the following requirements.

• Be at least 18 years of age at the time you file the application;Have been a lawful permanent resident for the past three or five years (depending on which naturalization category you are applying under);Have continuous residence and physical presence in the United States;Be able to read, write, and speak basic English;Demonstrate good moral character; (for five years before applying)Demonstrate a knowledge and understanding of U.S. history and government;Demonstrate a loyalty to the principles of the U.S. Constitution; andBe willing to take the Oath of Allegiance.

If you are removable from the United States due to conviction of an aggravated felony (a list of what is an aggravated felony is here), you can not be granted citizenship. Also, if you are removable for having committed crimes involving moral turpitude (CIMT), you can not become a citizen.

If, however, you have been convicted of a crime that does not make you removable, you can become a citizen after your sentence is complete. 

So the rule that controls applying for citizenship while on probation is 8 c.f.r. § 316.10(c)(1), which states:

Effect of probation or parole. An applicant who has been on probation, parole, or suspended sentence during all or part of the statutory period is not thereby precluded from establishing good moral character, but such probation, parole, or suspended sentence may be considered by the Service in determining good moral character. An application will not be approved until after the probation, parole, or suspended sentence has been completed.

So it appears from this that you may apply for citizenship while you are still on probation, but you can not naturalize, I.e., actually becomes a citizen until after your probation or parole is complete. So process seems to take a year or so to complete, so I would wait about a year or so before your probation is complete and then file the application.