We report a statistical analysis exploring the origin of the overall low star formation efficiency (SFE) of the Galactic central molecular zone (CMZ) and the SFE diversity among the CMZ clouds using a wide-field HCN $J$=4-3 map, whose optically thin critical density ($sim10^7,mathrm{cm}^{-3}$) is the highest among the tracers ever used in CMZ surveys. Logistic regression is performed to empirically formulate star formation probability of 195 HCN clumps, 13 of which contain star formation signatures. The explanatory parameters in the best-fit model are reduced into the virial parameter $alpha_{mathrm{vir}}$ without significant contribution from other parameters, whereas the performance of the model without $alpha_{mathrm{vir}}$ is no better than that using randomly generated data. The threshold $alpha_{mathrm{vir}}$ is 6, which translates into a volume density ($n_{mathrm{H_2}}$) of $10^{4.6},mathrm{cm}^{-3}$ with the $n_{mathrm{H_2}}$-$alpha_{mathrm{vir}}$ correlation. The scarcity of the low-$alpha_{mathrm{vir}}$ clumps, whose fraction to all HCN clumps is 0.1, can be considered as one of the immediate causes of the suppressed SFE. No correlation between the clump size or mass and star formation probability is found, implying that HCN $J$=4-3 does not immediately trace the mass of star-forming gas above a threshold density. Meanwhile, star-forming and non-star-forming clouds are degenerate in the physical parameters of the CS $mathit{J}$=1-0 clouds, highlighting the efficacy of the HCN $mathit{J}$=4-3 line to probe star-forming regions in the CMZ. The time scale of the high-$alpha_{mathrm{vir}}$ to low-$alpha_{mathrm{vir}}$ transition is $lesssim2$ Myr, which is consistent with the tidal compression and X1/X2 orbit transition models but possibly does not fit the cloud-cloud collision picture.
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