The first observation of the ${{{{\varXi } ^0_{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{\pi } ^+} }}$ decay and the most precise measurement of the branching fraction of the ${{{\varLambda } ^0_{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{K} ^+} }$ decay are reported, using proton-proton collision data from the LHCb experiment collected in 2016–2018 at a centre-of-mass energy of 13$\text {,Te\hspace{-1.00006pt}V}$, corresponding to an integrated luminosity of 5.4$\text {,fb} ^{-1}$. Using the ${{{{\varLambda } ^0_{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {\varLambda } }}$ and ${{{{\varXi } ^-{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} }}$ decays as normalisation channels, the ratios of branching fractions are measured to be $\begin{aligned} {\frac{{{\mathcal {B}}}({{{\varLambda } ^0{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{K} ^+} })}{{{\mathcal {B}}}({{{{\varLambda } ^0_{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {\varLambda } }})}}&= (1.17 \pm 0.14 \pm 0.08)\times 10^{-2} , ,\ {\frac{{{\mathcal {B}}}({{{{\varXi } ^0_{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} {{\pi } ^+} }})}{{{\mathcal {B}}}({{{{\varXi } ^-_{b}} !\rightarrow {{J \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} {{\varXi } ^-} }})}}&= (11.9 \pm 1.4 \pm 0.6)\times 10^{-2}, , \end{aligned}$ B ( Λ b 0 → J / ψ Ξ - K + ) B ( Λ b 0 → J / ψ Λ ) = ( 1.17 ± 0.14 ± 0.08 ) × 10 - 2 , B ( Ξ b 0 → J / ψ Ξ - π + ) B ( Ξ b - → J / ψ Ξ - ) = ( 11.9 ± 1.4 ± 0.6 ) × 10 - 2 , where the first uncertainty is statistical and the second systematic.