Probability for 3 points $a$, $b$, $c$ chosen from $N$ points given their sum is constant, such that $a+b\ge c$, i.e, it can form a triangle.

Question

Question:
$$x_1 + x_2 + ... +x_N = \text{constant}$$ Given only that $N$ and $\text{constant}$ are real numbers, $x>0$, $N\ge 2$.

Find probability of choosing 3 numbers $a$, $b$ and $c$ from $N$ numbers such that $$a+b\ge c$$ (i.e. it must form a triangle).

My solution:
I am trying to solve it using recursion as i have no mathematical knowledge about it,but i could not solve,
How to solve it mathematically.