We formalise definitions of ballot secrecy and ballot independence by Smyth, JCS'21 as indistinguishability games in the computational model of security. These definitions improve upon Smyth, draft '21 to consider a wider class of voting systems. Both Smyth, JCS'21 and Smyth, draft '21 improve on earlier works by considering a more realistic adversary model wherein they have access to the ballot collection. We prove that ballot secrecy implies ballot independence. We say ballot independence holds if a system has non-malleable ballots. We construct games for ballot secrecy and non-malleability and show that voting schemes with malleable ballots do not preserve ballot secrecy. We demonstrate that Helios does not satisfy our definition of ballot secrecy. Furthermore, the Python framework we constructed for our case study shows that if an attack exists against non-malleability, this attack can be used to break ballot secrecy.