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.
Yes, absolutely, all nitrate counts in solubility product regardless of source. The system cannot distinguish what a nitrate ion (or any dissociated species) was bonded to before it dissociated.