Gaussian Half-Space Probability

Let $X, Y \sim N(0, 1)$ be jointly normal with correlation $\rho \in (-1, 1)$. For constants $k \in \mathbb{R}$ and $b \in \mathbb{R}$: 1. Compute $P(Y > kX + b)$ in closed form. 2. Compute $P(Y > kX + b \mid X > x_0)$ in closed form by conditioning on $X$ and using the conditional normal distribution.