I was reading this question and one of the video clips in the question had an exchange between Tarkin and Vader that got me thinking:
VADER: He is here.
TARKIN: Obi-Wan Kenobi. What makes you think so?
VADER: A tremor in the Force. The last time I felt it was in the presence of my old master.
TARKIN: Surely he must be dead by now.
VADER: Don't underestimate the Force.
TARKIN: The Jedi are extinct. Their fire has gone out of the universe. You, my friend, are all that's left of their religion. [An intercom beeps, which Tarkin answers] Yes?
INTERCOM: We've received an alert in Section AA23.
TARKIN: The princess? Put all stations on alert!
VADER: Obi-Wan is here. The Force is with him.
TARKIN: If you are right, he must not be allowed to escape.
VADER: Escape is not his plan. I must face him alone.
--- Star Wars: A New Hope
Obi-wan Kenobi, at the time of ANH, was only 57 years old. He had defeated Anakin Skywalker on Mustafar and then disappeared. He hadn't been killed by Vader as so many of the other former Jedi who had survived Order 66 (and here) had, so why would Tarkin, considering his presumed knowledge of the Empire's interest in and files on extant Jedi (particularly those that he served with/under during The Clone Wars) have thought that a 57-year old Obi-wan Kenobi must have been dead by that point?