Who will inherit our mother's house if there are three siblings involved?

If she does not have a will, and your father is dead, then the house and her estate would pass to the children. Assuming there were only three children, then to the three. If there had been more children, and those children were dead, but they had children, those grandchildren step into their parent's shoes for the purposes of inheritance.

In Illinois, where the property is owned solely by the decedent and there is no will the assets are distributed in accordance with the Illinois statute on descent and distribution. After all creditors are paid, the remaining assets in the estate are distributed as follows: Where there is no living spouse but there are descendant of the decedent, then the assets are distributed equally among the children of the decedent. In the event one of the children predeceased the decedent then share that the predeceased child would have received if alive is divided equally among the descendants of that predeceased child; if there is a living spouse and descendants, then the spouse receives half of the assets and the children equally share half of the assets, with the descendants of a predeceased child dividing the share that the predeceased child would have received if alive; if there is a living spouse and no descendants then the living spouse receives all of the assets; if there is no living spouse and there are no descendants, then the assets are distributed equally among the parents and siblings of the decedent (if only one parent survives then that parent receives a double share), with the descendants of a predeceased sibling dividing the share that the predeceased sibling would have received if alive. In this case, where there is no living spouse and the decedent had only three children, born or adopted to her, and all the children are living, then the assets in the estate are divided into thirds. The house can be sold and the net proceeds divided among the three children or the house can be transferred to the children as Tenants in Common as to a one-third interest in the house. A probate will have to be opened to either sell the house or transfer it to the children.