Krattenthaler's 1/3-phenomenon conjecture for rhombus tilings

Let $a$, $b$, $c$, $x$ and $y$ be arbitrary integers. Consider a hexagon with side lengths $2n+a$, $2n+b$, $2n+c$, $2n+a$, $2n+b$, and $2n+c$, and a horizontal rhombus whose bottom-most vertex is $(2n+x,2n+y)$ in oblique angled coordinates. Krattenthaler's 1/3-phenomenon conjecture. For some $n_0$ depending on $a$, $b$, $c$, $x$ and $y$, the probability that a randomly chosen rhombus tiling of this hexagon contains the specified rhombus is

$$\frac{1}{3}+f_{a,b,c,x,y}(n)\frac{\binom{2n}{n}^3}{\binom{6n+2}{3n+1}},$$

for $n>n_0$, where $f_{a,b,c,x,y}(n)$ is a rational function in $n$. This conjecture generalizes Propp's observation about the near-central rhombus in a hexagon with all side lengths equal.