Say we're in a jurisdiction where noble titles are inherited on the basis of primogeniture. The holder of a noble title dies, and their closest surviving heirs are twin siblings for which there is absolutely no reliable evidence for the relative order of birth. (Perhaps the mother gave birth alone and then died before telling anyone which twin came first.) Let's further stipulate that the sex of the siblings does not come into play; either both siblings have the same sex, or else the jurisdiction does not favour one sex over the other when it comes to inheritance of titles. Both siblings want to assume the title. Unlike personal and real property, a noble title is indivisible and cannot normally be sold, so it's not possible to award the title, or half of its value on sale, to each claimant.
What does the law say about who inherits the title? If the law says nothing, and the siblings take the matter to court, on what basis would the matter be decided? Could the judge legally order the title to be awarded at random to one of the claimants?
I'm most interested in answers specific to British nobility, but would also be interested in hearing how this case would be handled in other jurisdictions.