Address the reason you were put on probation in the first paragraph of your letter. Give specifics so that the law school does not have to hunt down your records to understand why you are petitioning for readmission. For example, if you were suspended for a low grade point average, be specific: "I was put on probation from State Law School in December 2010 for having a grade point average of 1.65."
Explain why you are asking for reinstatement. Detail why you are now better equipped to succeed in law school than you were before you were put on probation. For example, if you experienced a death in the family that impacted your grades or ability to attend classes, explain the situation. Only use such an explanation if it is true; don't use it merely to elicit sympathy. If you simply were not focused on your studies at the time but you are now, say so.
Provide evidence that shows why the school should readmit you. If you have been interning at a law firm and demonstrated success and an interest in law, have your supervisor write a letter of recommendation that testifies to your hard work. In this paragraph, reference any supporting evidence that you will provide to show your commitment to succeeding in law school. Even if you don't have any documentation, discuss your renewed focus on law school coursework.
Compose a final paragraph with a call to action. State that you are confident that you can succeed in law school. Identify the semester in which you want to re-enroll in classes. Provide your contact information should the law school need to contact you. If you have any enclosures, like a letter of recommendation, mention it in this letter.