 SLE does not hit a fixed nonzero boundary point

For every $x\in \mathbb{R}\setminus \{0\}$, the probability that a chordal ${\mathrm{SLE}}_{\kappa }$ trace in $(\mathbb{H},0,\infty )$ passes through $x$ is zero. The SLE boundary-point logarithmic separation diffusion shows that the chance for $x$ to be swallowed strictly before a nearby point tends to zero as that point approaches $x$; Scaling invariance of SLE and reflection then handle every nonzero $x$.