The kinetic accessibility of various compact conformations of chain molecules is studied using a short self-avoiding chain on a three-dimensional cubic lattice. The kinetic accessibility of a compact conformation depends on the conformational energy and the distances from the other conformations along kinetically possible trajectories. We focus on the kinetic distances. We consider a chain in a poor solvent, having multiple lowest-energy compact conformations. The chain collapse from an arbitrary conformation to one of the lowest energy conformations is investigated. Though the lowest energy states would be occupied with the same probability in equilibrium, the probabilities for a first hit are not necessarily all the same and they indeed are not. We show that the hit probability at low temperature can be used as a measure of the kinetic distances from other conformations. The hit probability is investigated under two kinetic processes. One is a Monte Carlo dynamic process and the other is a ''contact-set stepping'' process, in which kinetic distances between conformations are defined based on sets of contacts. The two kinetic processes exhibit similar results showing that both processes well reproduce the kinetic behavior of chain molecules. Through the characterization of the states with large hit probability at low temperature, we show that the influence of the kinetic distances on the kinetic accessibility can be explained by domain structure or locality of contacts.