This paper presents a rigorous approach to calculate detailed site percolation probabilities in a rectangular n x m grid. The probability of finding a site in a particular grid point is allowed to be a function of the grid point location. It is shown that the exact site percolation probabilities can be obtained via a connectivity matrix. Notions of symbolic algebra further allow the site percolation probabilities to be expressed as polynomials, and their coefficients can be deduced exactly. It is shown that when the probability of finding a site in a grid point is independent of the grid point location, then long-range site percolation diminishes exponentially with the length of the grid, while the coefficient in the exponent is an explicit function of an eigenvalue of the connectivity matrix.