# Should I include ions from the solvent in solubility product constant calculations?

I'm trying to determine the Solubility Constant $$K_\mathrm{sp}$$ of $$\ce{Ba(NO3)2}$$ dissolved in nitric acid solution $$\ce{HNO3}$$ from experimental data.

$$\ce{HNO3}$$ will be mostly dissociated so there are many $$\ce{NO3-}$$ ions already in the solvent before solid $$\ce{Ba(NO3)2}$$ is added.

When I calculate $$K_\mathrm{sp} = [\ce{Ba^2+}][\ce{NO3-}]^2$$, do I include in $$[\ce{NO3-}]$$ the ions already present in the solution before solid $$\ce{Ba(NO3)2}$$ is added?

For example, say I have dissolved $${0.1 mol}$$ of barium nitrate in $${1 L}$$ of $${1 M}$$ nitric acid solution. There are now $${0.2 mol} + {1 mol} = {1.2 mol}$$ of nitrate ion in the solution. Should my $$K_\mathrm{sp}$$ calculation be

$$K_\mathrm{sp} = 0.1\cdot 0.2^2,$$

or

$$K_\mathrm{sp} = 0.1\cdot 1.2^2?$$

I understand that the common ion effect in this case inhibits solubility somewhat, but it I think my professor told me to include ions from $$\ce{HNO3}$$ in the calculation, which seems wrong.