It will be critical to your case that you have a lot of proof that you entered into the marriage in good faith. You really need the help of an immigration attorney.
It is your requirement to prove to USCIS that your marriage was bonafide. If you manage to do that, then your conditions will be removed. You should absolutely retain an immigration attorney to help you with this process. Good Luck.
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What are the chances? Well, it depends on all the facts of this particular case, including the proofs that the marriage was legitimate. Representation is strongly suggested.
Disclaimer: This answer is for informational purposes and does not take the place of a consultation with an experienced immigration attorney. This answer does not create an attorney-client relationship.
Would the person get their Green Card? It is impossible for any attorney to be sure as it would be adjudicated by a third party, the USCIS. However this person would most likely be eligible to apply to have the conditions removed from their Green Card. They would need to prove that the marriage was real and entered into in good faith and they would prove that through evidence. I would strongly recommend that this person retains an attorney to help them present the strongest case possible for them.