For sustainable advancements in electronics technology, the field of neuromorphic electronics; i.e., electronics that imitate the principle behind biological synapses with a high degree of parallelism has recently emerged as a promising candidate for novel computing technologies. In this study, we designed and fabricated a vertical form of a gate-tunable binary Si switching device using a SiO_x memristor in combination with graphene barrister, which is inspired by tunable and probabilistic synaptic signaling processing of the rod-to-rod bipolar cells in the human visual system. The device architecture can function as a changeable probabilistic artificial synapse that can be utilized as the basic component of the sparse neural network capable of low-power and learning acceleration for recognizing images. We also developed a drop-connect algorithm that can reflect the sparse connectivity in the biological neural network, and then evaluated the recognition accuracy and the consuming energy for several fashion items according to the probabilistic degree of Si synaptic activity in the drop-connect neural network. In this result, our suggested probabilistic Si synapse and the drop-connect network could offer a distinctive and novel strategy of a neuromorphic computing system equipped with low-power and learning acceleration.