There is no such thing as a "reading" of a will. This is something that happens only in films and literature.
The will only becomes a public document on probate being granted. Generally probate is only necessary for estates over �5k (although I have managed for several estates under �15k).
However, once death occurs and the will is found, the executors will undoubtedly start work on ascertaining the assets and liabilities - indeed they need to do so before organising the funeral to ensure there are sufficient assets to cover the funeral costs.