If the probation department is behind you the odds are pretty good in most courts. Two things can help: 1. Get letters if good character and have your attorney give them to the judge. 2. Speak at your sentencing and explain how embarrassed and remorseful you are and how you will never do it again.
There is not enough information to be able to answer the question accurately. The attorney handling the case should have the information to do so. I agree that if probation is recommending house arrest, it is favorable; my question though, is whether this is for a bail hearing, or for sentencing? "Armed robbery" is a very serious offense, and if if really involves a firearm the consequences can be dramatic depending on the facts, and usually leads to custody time. But these cases are resolved many times by plea agreements that lessen the potential consequences and charges. Again, the attorney handling the case is the one to whom you should ask this specific question.
If probation is recommending probation then you may have a good chance. You should be speaking with your attorney about this. S/he is in the best position to advise and guide you.