person, a legal resident of Alaska, owns real estate in three States--Alaska, Washington (state),and Florida--died while temporarily living in Florida

Wow that's a tough one. There will be some sort of probate action in each state that real estate was owned. The main question is where to start.  The question of one's legal residence becomes the key issue. If Florida was truly temporary then I would probably start in Alaska and make that the domiciliary estate.  Then I would open ancillary probates in Washington and Florida.  I would suggest you talk to a Florida probate attorney as well as an Alaska probate attorney to determine if there are advantages to starting the probate in one state versus the other. You have a complex situation on your hand. Too bad the decedent didn't have a living trust as that would have saved a lot of trouble here!  Good luck to you.