Probate should not be necessary for the property if you believe your mother intended to give the non-family member a the life estate. If you have issues with that contract, you should meet with a local probate attorney to discuss options.
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My guess is that the purchaser's interest in a land contract would be considered an asset of the estate. It is possible, depending on how this was structured, that the interest that your mother had terminated upon her death, in which case, there would be nothing to include in probate and equitable title in the property interest would pass to the heirs. This sounds like an unusual arrangement, however, and the documents should be reviewed by a probate attorney to be sure you are proceeding correctly.
The Will provision can only be given effect through probate. A contract provision may take it out of probate, however.
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I do think you will need to probate your mother's estate as she was the seller under a contract for deed that has not yet been completed. It is only when the contract is paid in full that the seller supplies equitable title to the buyer via deed. Someone will need authority as personal representative to sign the deed completing the contract. Or, if 3 years has passed since her death, you could obtain a decree of descent for the transfer of the property to the buyers. I would definitely consult a probate attorney regarding same.