Defectless polynomials over henselian fields and inductive valuations

Let $(K,v)$ be a henselian valued field. Let ${\mathbb{P}}^{dless}\subset K[x]$ be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation $\approx$ on ${\mathbb{P}}^{dless}$, we establish a canonical bijection $$\mathbb{M}$\to $\mathbb{P}$^{dless}/!!\approx$,where$$\mathbb{M}$$ is a discrete MacLane space, constructed in terms of inductive valuations on $K[x]$ extending $v$.