We study the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ using $117\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ events collected at the $Y(4S)$ resonance with the BABAR detector at the PEP-II ${e}^{+}{e}^{\ensuremath{-}}$ asymmetric-energy storage ring. We measure the branching fractions $\mathcal{B}$ $({B}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(116\ifmmode\pm\else\textpm\fi{}7(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}9(\mathrm{syst}.))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $\mathcal{B}$ $({B}^{\ensuremath{-}}\ensuremath{\rightarrow}X(3872){\mathrm{K}}^{\ensuremath{-}})\ifmmode\times\else\texttimes\fi{}$ $\mathcal{B}$ $(X(3872)\ensuremath{\rightarrow}\mathrm{J}/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})=(1.28\ifmmode\pm\else\textpm\fi{}0.41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and find the mass of the $X(3872)$ to be $3873.4\ifmmode\pm\else\textpm\fi{}1.4\text{ }\text{ }\mathrm{MeV}/{\mathrm{c}}^{2}$. We search for the ${h}_{c}$ narrow state in the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}_{c}{K}^{\ensuremath{-}}$, ${h}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and for the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{D}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}$, with ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$. We set the $90%$ C.L. limits $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}{h}_{c}{K}^{\ensuremath{-}})\ifmmode\times\else\texttimes\fi{}\mathcal{B}({h}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})<3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ and $\mathcal{B}({B}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{D}^{0}{\ensuremath{\pi}}^{\ensuremath{-}})<5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$.
