We report the observations of J = 1-0 of HCN, HCO+, (HCO+)-C-13, and (HCN)-C-13, HC3N (J = 11-10) emission towards 135 massive star-forming clumps, as part of the ALMA Three-millimeter Observations of Massive Star-forming regions Survey. We present the integrated intensity probability distribution function (I-PDF) for these molecular tracers, modelled as a combination of a lognormal distribution and a power-law tail. The molecular line luminosities for the power-law tail segment, Lmol(p), have been calculated. We have investigated the correlation between the bolometric luminosity, L-bol, and the power-law part of the molecular line luminosity, L-mol(p). Our findings suggest that the scaling relationships between L-bol and L-mol(p) for HCN and HCO+ are sublinear, indicating that these molecules might not be the most effective tracers for the dense gas. In contrast, (HCN)-C-13 and HC3N exhibit a nearly linear relationship between L-bol and L(mol)l(p), indicating that they can well trace gravitationally bound dense gas. The ratios of L-bol-to-L-mol(p), serving as indicators of star formation efficiency (SFE) within massive star-forming clumps, exhibit a weak anticorrelation with the power-law index in the I-PDF. In addition, the SFE is also weakly anticorrelated with the exponent alpha of the corresponding equivalent density distribution. Our results implie that clumps with substantial gas accumulation may still display low star formation efficiencies.