The dynamics of aqueous Laponite clay suspensions slow down with increasing sample waiting time (t w ). This behavior, and the material fragility that results, closely resemble the dynamical slowdown in fragile supercooled liquids with decreasing temperature, and are typically ascribed to the increasing sizes of distinct dynamical heterogeneities in the sample. In this article, we characterize the dynamical heterogeneities in Laponite suspensions by invoking the three-point dynamic susceptibility formalism. The average time-dependent two-point intensity autocorrelation and its sensitivity to t w are probed in dynamic light scattering experiments. Distributions of relaxation time scales, deduced from the Kohlrausch-Williams-Watts equation, are seen to widen with increasing t w . The calculated three-point dynamic susceptibility of Laponite suspensions exhibits a peak, with the peak height increasing with evolving t w at fixed volume fraction or with increasing volume fraction at fixed t w , thereby signifying the slowdown of the sample dynamics. The number of dynamically correlated particles, calculated from the peak-height, is seen to initially increase rapidly with increasing t w , before eventually slowing down close to the non-ergodic transition point. This observation is in agreement with published reports on supercooled liquids and hard sphere colloidal suspensions and offers a unique insight into the colloidal glass transition of Laponite suspensions.