The markets – that is, domestic and foreign savers/creditors, plus any speculators/anticipators – read the papers, watch TV and follow social media, listen to policy statements and try to understand whether the probability of a State default is increasing or decreasing.
For a country that is a member of the euro area, like Italy, they also look at its relationship with the European institutions and EU legislation, because any 10  deterioration in these relationships is a sign of an approaching expectation of a default, even a unilateral abandonment of the euro area. Therefore Europe is important, but only indirectly.