It's a bit incorrect. Basic formula is (1-k/n)^n ~ exp(-k) when n is sufficiently large (mathly speaking lim of the left term when n grows to infinity is exp(-k)). In the papers, you get quantities like (253/256)^(256-p-1) (probability the (256-p-1) bytes of the KSA are different from 3 given values), with p=3,... First you approximate the exponent with 256, and you rewrite (1-3/256)^256, which then you approximate with the limit exp(-3).
cf
http://mathworld.wolfram.com/ExponentialFunction.html