Predicting future motions of surrounding vehicles and driver's intentions are essential to avoid future potential risks. The predicting future motions, however, is very challenging because the future cannot be deterministically known a priori and there are infinitely many possible future trajectories. Prediction becomes far more challenging when trying to foresee distant future. This paper proposes a probabilistic motion prediction algorithm that can accurately compute the likelihood of multiple target lanes and trajectories of surrounding vehicles by using the artificial neural network; more specifically radial base function network (RBFN). The RBFN prediction algorithm estimates the likelihood of each lane being the driver's target lane in categorical distributions and the corresponding future trajectories in parallel. In order to demonstrate the effectiveness of the proposed prediction algorithm, it is applied for the predictive cruise control problem. Chance-constrained model predictive control (CCMPC) is utilized because the chance constraints in CCMPC can handle collision uncertainties associated with future uncertainties from the proposed prediction algorithm. The RBFN-based CCMPC simulation is conducted for several risky cut-in scenarios and compared with the state-of-the-art Interactive Multiple Model (IMM)-based prediction algorithm. The simulation results show that the RBFN-based CCMPC achieves higher collision avoidance success rate than that of the IMM-based CCMPC while using smaller actuator inputs and providing higher passenger comforts. Furthermore, the RBFN-based CCMPC showed high robustness to false braking during near lane-change (lane-keeping) scenarios.