In our previous works, we have analyzed the two-body strong decays of
the low-lying $\Omega$ baryon states within a chiral quark model. The results show that the mass, total width, and two body decay $\Omega(2012) \to \bar{K}\Xi$ can be well reproduced with the spin-parity $J^P=3/2^-$ state $\Omega^*|1P_{3/2^-}\rangle$ classified in the quark model.
Stimulated by the new observations of the three-body decay process $\Omega(2012)^-\to \Xi^*(1530)^0K^-\to \Xi^-\pi^+K^-$ at Belle,
in the present work we further study the three-body strong decay $\Omega^*|1P_{3/2^-}\rangle \to \Xi^*(1530)\bar{K} \to \Xi\pi\bar{K}$
within the chiral quark model. It is found that the $\Omega^*|1P_{3/2^-}\rangle$ has a sizeable decay rate into the three-body final states $\Xi\pi\bar{K}$. If considering $\Omega^*|1P_{3/2^-}\rangle$ as the $\Omega(2012)$ resonance, the predicted ratio $R_{\Xi\bar{K}}^{\Xi\pi\bar{K}}=\mathcal{B}[\Omega^*|1P_{3/2^-}\rangle\to \Xi^*(1530)\bar{K}\to \Xi\pi\bar{K}]/\mathcal{B}[\Omega^*|1P_{3/2^-}\rangle \to \Xi\bar{K}]\simeq 12\%$ is close to the up limit $11\%$ measured by the
Belle Collaboration in 2019, however, it is too small to be comparable with the recent measurements $0.97 \pm 0.24\pm 0.07$. On the other hand,
the coupled-channel effects on the bare three-quark state $\Omega^*|1P_{3/2^-}\rangle$ from nearby channels $\Xi \bar{K}$, $\Omega\eta$ and $\Xi^*(1530)\bar{K}$ are also studied. Our theoretical results show that the coupled-channel effects on the $\Omega^*|1P_{3/2^-}\rangle$ are not very large, the molecular component is no more than $30\%$. To clarify the nature of $\Omega(2012)$ resonance, precise measurements on the ratio $R_{\Xi\bar{K}}^{\Xi\pi\bar{K}}$ are needed, and further investigation on the effects of coupled channels is most welcome. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.