The adsorption of proteins and other large molecules at the liquid-solid interface often involves a surface-induced transition in either internal conformation or molecular orientation. Recently, Van Tassel et al. modeled this adsorption/transition process as the sequential surface placement of spreading disks. In this work, we employ the scaled particle theory (SPT) to derive approximate analytical expressions for the probability functions appearing in the kinetic equations for this model system. Specifically, the probability functions governing the adsorption and spreading events are calculated in terms of the reversible work required to create cavities in a binary system of spread and unspread disks. Compared to those derived earlier via a density expansion theory (DET), the SPT approximated probability functions are simpler and more accurate (compared to simulation), and are applicable over a wider set of parameter values.