Final answer:
The most probable outcome is that Old Man Smith's sister's children would inherit the property under state intestacy laws since he died intestate, meaning without a will. The property would be distributed to his closest surviving relatives as determined by the hierarchy established by these laws.
Step-by-step explanation:
When Old Man Smith died without a will, he is considered to have died intestate. This means that the inheritance of his assets, including his property valued at $500,000, will be determined by the state's intestacy laws. In most cases, the laws of descent will be applied to determine the rightful heirs. Typically, the estate would pass to the closest relatives based on the hierarchy established by law which may include his sister and her children, as Smith never married and had no direct descendants of his own.
Therefore, it is likely that the sister's children, being Smith's closest surviving relatives, could inherit the property under state intestacy laws, making option (a) the most probable outcome. It is important to consult the specific state laws to determine the exact division of the estate among the heirs.