The intercombination $a^3Pi - X^1Sigma^+$ Cameron system of carbon monoxide has been computationally studied in the framework of multi-reference Fock space coupled cluster method with the use of generalized relativistic pseudopotential model for the effective introducing the relativity in all-electron correlation treatment. The extremely weak $a^3Pi_{Omega=0^+,1} - X^1Sigma^+$ transition probabilities and radiative lifetimes of the metastable $a^3Pi$ state were calculated and compared with their previous theoretical and experimental counterparts. The impact of a presumable variation of the fine structure constant $alpha=e^2/hbar c$ on transition strength of the Cameron system has been numerically evaluated as well.
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