Even if a will is left, and acted on by the executor, it doesn't always follow that probate has to be applied for.
It depends on what (if anything) the person had as assets when they died. With smaller estates, an executor can often deal with the will, and distribute the proceeds, without having to make an application for probate and in that case there will be no record of the will at all beyond any copies held by the executor/family.
Ownership of a property would normally need probate to deal with, but even that may not if it was held as joint owners with someone and therefore passes automatically to the survivor's sole ownership.
Same with administration where no will is left -a family member could deal with a small estate without leaving any record.