1. A running support system for a vehicle, comprising: a first object detecting portion that detects an object near the vehicle using a radar; a second object detecting portion that detects the object near the vehicle by performing image recognition based on an obtained image of an area near the vehicle; and a running support portion that supports running of the vehicle, wherein a control condition for running support control performed by the running support portion is changed on the basis of an evaluation whether the same object has been detected by (i) only the first object detecting portion, (ii) only the second object detecting portion, or (iii) both the first object detecting portion and the second object detecting portion; and wherein a probability that the object exists is calculated to be the highest when both the first object detecting portion and the second object detecting portion detect the object, the next highest when only one of the first object detecting portion or the second object detecting portion detects the object, and the lowest when neither the first object detecting portion nor the second object detecting portion detects the object, and the control condition is changed in accordance with the calculated probability.