Usually, the laws of the state in which the deceased was last a permanent resident prevail in regard to governance of probate issues - covering all of the deceased's personal property, wherever it was located, and all the deceased's real property located within the state. Therefore, probate almost always filed in the last state where the deceased person lived.
If the decedent owned out-of-state real property, the laws of the other state can govern (or certainly affect) who inherits it if there is no will. If a will exists and it has been filed for probate in the state of most recent residence of the deceased, it usually must be submitted to probate in the other state(s) of jurisdiction in which the deceased owned real property.
That additional probate filing is formally referred to as "ancillary probate". Some states require the appointment of a personal representative who is a local resident or the state to administer any in-state property.
If there is no Will, probate is usually required in each state where the real property is situated, in addition to the home state and each individual state can impose its own methodology that controls the distribution of assets. As an example, in one state, the real estate might go only to the spouse. In another state, like Texas, it might be equally divided between a spouse and each of his or her children. In still another, half of the assets might go to a spouse and the remainder divided equally between the children. This is one of the reasons a will is so important to properly express the wishes of the deceased and prevent family struggles and quarrels following a death.