Bitul B4 pesach

Question

I understand the concept of bitul (bitul b'rov, bitul b'shishim) that exists before Pesach. With Chametz this does not exist during Pesach as chametz is oser b'mahshehu (prohibited with the smallest amount). If I have a pot which is chametzdik (used throughout the year for, say, making chicken soup). I thoroughly clean it so that there is no residue left. Now I use this pot to prepare chicken soup for Pesach. Is there anything wrong with this procedure since I can rely on bitul for any chametz that may derive from the walls of the pot (nosain tam). I have no intention of using the pot during Pesach.