The Lindy effect [1] and the doomsday argument [2] are sort of corollary to your use of the principle of indifference.

p(doom) may be 50%, but the future life expectancy of humanity is at least several thousand years with 95% confidence.

[1]: https://en.wikipedia.org/wiki/Lindy_effect

[2]: https://en.wikipedia.org/wiki/Doomsday_argument