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Triadic closure is the smallest unit of social network analysis building blocks. It helps to interpret the underlying nature of network behaviour and dynamics. Triadic closures may or may not depend on the social influences. In this paper, we have shown an extended theory to measure the probabilistic formulation of triadic closure. Our proposed Probabilistic triadic Model depends upon the probability of social influences which was missing in the existing theories. We have introduced a new parameter called index of inclination for the probability of triadic closure formation. Observations are analysed and it shows how our probability relation between triadic closures or the link formation and social influences precisely interprets all the social networking scenarios.