We present a Bayesian probabilistic model---termed the Enhanced Cosmic Life Probability Estimator (ECLPE)---to quantify the likelihood of life in the observable universe. The framework extends the classical Drake equation by representing each astrobiological factor as a random variable with empirically informed prior distributions. Crucially, we integrate real exoplanet data from the NASA Exoplanet Archive (as of January 2026) via the astroquery interface and update the atmospheric retention probability f_atm using James Webb Space Telescope (JWST) observations. Monte Carlo simulations (200,000 iterations) yield posterior distributions for both microbial and intelligent life. A variance-based global sensitivity analysis using Sobol indices identifies the dominant sources of uncertainty. The independence assumption among factors is a statistical simplification, with potential correlations addressed in sensitivity tests. Our results indicate that while simple life is statistically probable across cosmic scales, detectable technological civilizations remain exceedingly rare. The model is fully reproducible and open-source, designed for iterative refinement as new data emerge.