Actually, I expected Gott equation to be mentioned here, as his Doomsday argument is a contemporary version of Laplace equation.
Also, qualified observers are not distributed linearly inside this period of time: from the idea of AI to creation of AI. If we assume that qualified observers are those who are interested in AI timing, than it look like that such people are much more numerous closer to the end of the period. As result, a random qualified observer should find oneself closer to the end of the period. If the number of qualified observers is growing exponentially, the median is just one doubling before the end. This makes AI timing prior closer to current events.