An idealized linear collision model has been employed to calculate the reaction probabilities for the three-atom rearrangement reaction $A+B-C{ o}A-B+C$. Potential energy surface used is also a highly idealized one with constant values. Numerical results were obtained for the system in which the atomic masses of all three atoms are the same. Potentials were varied to see the effect of the magnitude of the opposing potential barrier on the reaction probabilities. Results obtained were compared with those obtained using different models.