Kathleen,
Finding the entry in the Probate Index (from Ancestry or the Genealogist?) was good but I think you have mis-interpreted what it says.
1964 - "SKINNER David of 30 Marion Street Birkenhead died 15 October 1964 at St Catherine Hospital Annexe Birkenhead Administration Liverpool 6 November to Gladys May SKINNER widow. £469."
If there was a Will then the executor named in the Will would have been granted "Probate". The fact that Gladys was granted "Administration" means that there was no Will.
When a person is granted "Probate" then they don't inherit all the property of the deceased. They get the authority to sort out the affairs of the deceased and to share out the deceased's property in accordance with the terms of the Will.
When there is a Will then a copy can be obtained here.
http://www.justice.gov.uk/courts/probate/copies-of-grants-wi...When a person is granted "Administration" then they are still not free to do whatever they want with the property. In the absence of a Will there are rules about how the property is shared between wives, children, the Government etc.
Bryan