Install "Kindle for PC". Go to the "Archive" on "Kindle for PC" and download the book; that will download it to your PC, and put it in the "My Documents\My Kindle Content" folder. Open Windows Explorer and drag it from there into Calibre.
Note: the filename on the PC will be a meaningless string of numbers. To find which is the correct book to copy to Calibre, sort the folder by date and then look for the book file that has a timestamp of the date and time that you downloaded it. You can double-click it in Windows Explorer to open it in K4PC and verify that it really is the correct book.
Currently proofreading The Poison Belt, by Sir Arthur Conan Doyle.