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Motivated by the recent discovery of two new states in the $B^+\rightarrowD^+D^-K^+$ decay by the LHCb Collaboration, we study the $D\bar{D}K$ three-bodysystem by solving the Schr\"odinger equation with the Gaussian ExpansionMethod. We show that the $D\bar{D}K$ system can bind with quantum numbers$I(J^P)=\frac{1}{2}(0^-)$ and a binding energy of$B_3(D\bar{D}K)=48.9^{+1.4}_{-2.4}$ MeV. It can decay into $J/\psi K$ and$D_s\bar{D}^*$ via triangle diagrams, yielding a partial decay width of about 1MeV. As a result, if discovered, it will serve as a highly nontrivial check onthe nature of the many exotic hadrons discovered so far and on non-perturbativeQCD as well. Assuming heavy quark spin symmetry, the same formalism is appliedto study the $D\bar{D}^*K$ system, which is shown to also bind with quantumnumbers $I(J^P)=\frac{1}{2}(1^-)$ and a binding energy of$B_3(D\bar{D}^*K)\simeq 77.3^{+3.1}_{-6.6}$ MeV, consistent with the results ofprevious works.

Excited $K$ meson, $K_c(4180)$, with hidden charm as a $D\bar{D}K$ bound state