We study a strongly interacting array of Bose-Einstein condensates trapped in a one-dimensional (1D) optical lattice. The system is described by a nonstandard 1D Bose-Hubbard model in which both the tunneling matrix element and the on-site atomic interaction depend on the lattice site due to the interaction broadening of the local wave function and the system inhomogeneity. We quantitatively compare theoretical analyses based on the Gutzwiller approximation with experimental observations obtained using ytterbium atoms. We show that atomic states are highly number squeezed owing to strong interatomic interactions as the lattice potential becomes deeper. Furthermore, the calculated inhomogeneous collisional broadening of spectroscopic line shapes agrees well with high-resolution spectra measured by using the ultranarrow magnetic quadrupole S-1(0)-P-3(2) transition.