Suppose I die and, on the day before, I have signed two wills with conflicting terms.
If, for some reason, it is not possible to determine which of these was signed first, which terms will prevail? How is this decided?
In most places I imagine the issue would go before a probate judge who would attempt to determine the validity of each presented will, and if both were valid, then they would attempt to reconcile the disparities to the best of their ability.
Broadly speaking, the process would look like this (I'm using UK law as an example):
That being said, every jurisdiction is different, and this is more of a template answer for English common law (and derivative courts), than an attempt to describe in detail any specific jurisdiction's procedures.