Let $P_{x,w}$ be the Kazhdan–Lusztig polynomial, $\rho$ be the half sum of positive roots in $\Phi^+$, $M_x$ be the Verma module with highest weight $x\cdot(-2\rho)$ and $L_w$ be the simple highest weight module with highest weight $w\cdot(-2\rho)$.

It is well-known that Kazhdan–Lusztig Conjecture is equivalent to $P_{x,w}(q) = \sum_{i\ge 0}q^i \dim \mathrm{Ext}_\mathcal{O}^{\ell(x,w)−2i}(M_x, L_w)$ for all $x\le w$. And it is also well-known that Kazhdan–Lusztig Conjecture is true.

**My question:**
Does $P_{x,w}(q) = \sum_{i\ge 0}q^i \dim \mathrm{Ext}_\mathcal{O}^{\ell(x,w)−2i}(M_x, L_w)$ even for all $x\not\le w$?

If the answer is yes, any reference about that would be appreciated. If the answer is no, I would like to know why.