1. A traffic lane marking recognition apparatus comprising: a candidate detecting unit, using a processor, that detects a lane dividing line candidate which is a candidate for a lane dividing line that defines a traffic lane on a road, based on an image of the road captured by an on-board camera that is mounted in a vehicle; a gap detecting unit, using a processor, that detects a gap in the lane dividing line candidate detected by the candidate detecting unit; and a recognition reducing unit, using a processor, that when the gap is detected by the gap detecting unit, reduces a probability of recognition of the lane dividing line candidate as a lane dividing line to a first probability that is lower than the probability when the gap detecting unit does not detect the gap, in a region from the gap closest to the vehicle towards a direction away from the vehicle, the probability of recognition defining a probability that the lane dividing line candidate detected by the candidate detecting unit is a lane dividing line of the road, wherein recognition of the lane dividing line candidate as the lane dividing line of the road is based on the probability of recognition.