The other reason the Don might have been slightly slower to see Barzini's involvement was the Don's prejudice against such "dirty" businesses as drugs and prostitution.
Since Sollozzo was a former pimp and Tattaglia was deeply involved in pandering, the Don may have simply conflated both vices together and not seen past Tattaglia's involvement, for whom he obviously had no respect.
The Don might have had these thoughts:
"This narcotics business is just the sort of infamia a man like Tattaglia would be involved in. Barzini's no friend of mine but he's no fool either. He's too smart to waste his time backing a drug peddler like Sollozzo. But Tattaglia is greedy and stupid."
"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming
Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.
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