what is the probability of being in the top 2 of 70 contestants for 3 consecutive years?

Question

our football team has finished 2nd place out of 70 teams the past 3 years.  Although these are not random events, I would like to use random probablity as a benchmark of how rare such an occurrence is.

Answer 1

If the probability of being in any particular position in a league of 70 teams is strictly random, then there is a 1/70 chance of being first and a chance of 69/70*1/69 of not being first but of being second. This is 1/70! For this to happen for three consecutive years the chance is (1/70)^3=1/343000=0.000003 approx. (0.0003%). This is the same chance as being first for 3 years or last for 3 years, in other words, to be in the same position for 3 years, because only random chance is involved, and it is 100% certain that a team will be placed in rank 1 to 70.

The probability of being either first or second is slightly different. The possibilities are 2*1/70=1/35 and over 3 years it's 0.000023 (0.0023%).