Typical companies last about 10 years: "the typical half-life of a publicly traded company is about a decade".
Kongo Gumi was a company founded in 578, and was still in operation when it was bought in 2006.
Laplace's rule of succession is a rule of thumb to generate a probability for something that hasn't ever happened. 0 is not a probability, so if the sun has risen a thousand times, one should estimate the probability of it not rising as 1/(n+1) = 1/1001.
One should expect long-lived companies to last longer. It is not just chance that they survived. But one's estimate of their life expectancy should not increase forever. The naive Lindy effect says a 1000-year-old company has a 50% chance of lasting another 1000 years. In reality, it is less than 50%. I would expect that the rate of increase in life expectancy to reduce, until life expectancy remains constant. Perhaps a 1000-year-old company can only be expected to live another 50 years. That's still much higher than a typical company!