The points fall evenly inside the rectangle $a \times b$. The centre of the rectangle is in $(0,0)$.
Every time each point is approximated with two parameters: $p_1$ and $p_2$ so that $$|p_1| + |p_2| = c = const$$
and $$L = (p_1-x)^2 + (p_2-y)^2 \to min$$
What will be the probability of that $p_1 \cdot p_2$ $\neq 0$ ?
I had only one idea - to use LASSO regression Tibshirani but could not count probability. Maybe you have some ideas?