You need to get the file downloaded to your computer by sending it to the
Kindle for PC (or Mac) application from Amazon. So download the free app to your computer, register it to your Amazon account, and send the book from your Amazon library (Manage Your Kindle page) to the Kindle for PC/Mac app. When you buy future books from Amazon you'll be able to select the Kindle for.... app and send the file directly to your computer. You'll find the book file (.azw suffix) located on your computer in the My Kindle Content folder that corresponds with the Kindle for PC (or Mac) app.
Now you can add the .azw book file to calibre and convert the format from mobi to epub to use on your Sony. Note: if the ebook has DRM protection, then you'll need the plugins from Apprentice Alf added to calibre in order to free the file so you can do a conversion.