Vanishing probability conjecture for fixed knots in the Chebyshev billiard model

Let $T(3,n+1)$ be the random knot model obtained from Chebyshev billiard table diagrams, and let $P(T^{(n)}_K)$ denote the probability that the resulting diagram represents a fixed knot $K$. Vanishing probability conjecture. The probability

$$P(T^{(n)}_K)$$

of obtaining $K$ in the model $T(3,n+1)$ goes to $0$ as $n$ approaches infinity. This is conjectured from numerical computations because no closed formula for $P(T^{(n)}_K)$ is available; the claim concerns the asymptotic behavior of each fixed knot in this random model.