The strange axial-vector mesons ${K}_{1} (1270)$ and ${K}_{1} (1400)$ are reanalyzed in the light of the updated experimental information and compared with the recent result on the $K\ensuremath{\pi}\ensuremath{\pi}$ production in $\ensuremath{\tau}$ decay. The mixing angle between the strange mesons of $^{3}P_{1}$ and $^{1}P_{1}$ is determined by the partial decay rates, and, independently, by the masses. They lead to ${\ensuremath{\theta}}_{K}\ensuremath{\approx}33\ifmmode^\circ\else\textdegree\fi{} or 57\ifmmode^\circ\else\textdegree\fi{}$. The observed ${K}_{1} (1400)$ production dominance in the $\ensuremath{\tau}$ decay favors ${\ensuremath{\theta}}_{K}\ensuremath{\approx}33\ifmmode^\circ\else\textdegree\fi{}$. Flavor-SU(3) breaking of 20% or so in the production amplitudes can explain quantitatively the observed production ratio.