Distribution of a random variable given on the set of all natural number if ...

What is the distribution of a random variable $xi$ given on the set of all natural numbers, if $$mathbb P(xi > a + b mid xi > a) = mathbb P(xi > b)$$ $$forall a,b in mathbb N$$

Simplifying the equality, I got $$mathbb P(xi > a + b) = mathbb P(xi > a) mathbb P(xi > b)$$ because $$mathbb P(xi > a + b mid xi > a) = frac{mathbb P(xi > a + b cap xi > a)}{mathbb P(xi > a)} = frac{mathbb P(xi > amid xi > a + b)mathbb P(xi > a + b)}{mathbb P(xi > a)} = frac{mathbb P(xi > a + b)}{mathbb P(xi > a)}$$

After a little thought, I realized that the distribution can be $$S = sum_{i=1}^n frac{1}{2^n}$$ $$lim_{nto infty}S = 1 = p_1 + p_2 + ldots + p_n + ldots$$

But I want to know if it is possible to generalize somehow and find all such distributions and show that there are no others. Thanks.