The answer will depend on how the house is titled. There are ways to avoid costly probate by spending a little money on probate planning in advance. I would contact Ward and Lee in Vinita at 918-323-9100 or another attorney in your area that handles probate law and speak with them. They will probably offer a free consultation which you should consider.
You don't mention whether your mother also lives in Oklahoma, and the state of her residence will make a difference in how your question is answered. The smartest thing to do is to consult a qualified estate planning lawyer who practices where your mother lives. Many attorneys do not charge for the initial consultation, and the advice you will receive could be invaluable.
To get started, if your mother does live in Oklahoma, I suggest you consult the information about the probate process that is published by the Oklahoma Bar Association through the link provided here.
This answer does not constitute the provision of legal advice nor does it establish an attorney/client relationship of any kind.