We present a functional integral formulation of the probability distribution of the worm-like polymer chain which not only takes into account the skeletal stiffness but also explicitly includes the differentiability condition of Kratky and Pored while remaining mathematically tractable. We get closed form expressions for the probability distribution of loops of size L unlike the previous work of Yamakawa et al. [J. Chem. Phys. 57, 2843 (1972)] which gave the results as an infinite series.