In the UK, when a Grant of Probate or a Grant of Letters of Administration is issued by the Probate Registry it becomes a public document. Meaning that the document itself can be viewed, if it is a Grant of Probate then there will also be an associated Will that can be downloaded to view or a copy ordered from the public records.
There are currently specific rules in place surrounding the privacy of Wills of Senior members of the Royal Family who have passed away, the most recent one being the Will of The Duke of Edinburgh. These rules were put in place more than 100 years ago and the first Royal whose Will was made secret, and which still does to this day, was Prince Francis of Teck, the brother of Queen Mary. The reasons surrounding this specific ruling and how it all began can be read by clicking on the link below.