  We study the fragmentation fractions $(f_{{\bf B}_b})$ of the $b$-quark to
b-baryons (${\bf B}_b$). By the assumption of $f_{\Lambda_b}/(f_u+f_d)=0.25\pm
0.15$ in accordance with the measurements by LEP, CDF and LHCb Collaborations,
we estimate that $f_{\Lambda_b}=0.175\pm 0.106$ and $f_{\Xi_b^{-,0}}=0.019\pm
0.013$. From these fragmentation fractions, we derive ${\cal B}(\Lambda_b\to
J/\psi \Lambda)=(3.3\pm 2.1)\times 10^{-4}$, ${\cal B}(\Xi_b^-\to J/\psi
\Xi^-)=(5.3\pm 3.9)\times 10^{-4}$ and ${\cal B}(\Omega_b^-\to J/\psi
\Omega^-)>1.9\times 10^{-5}$. The predictions of ${\cal B}(\Lambda_b\to J/\psi
\Lambda)$ and ${\cal B}(\Xi_b^-\to J/\psi \Xi^-)$ clearly enable us to test the
theoretical models, such as the QCD factorization approach in the $b$-baryon
decays.
