Probabilities having rational mass at finitly many rational points are dense in $\mathcal{P}(\mathbb{R})$

Question

we know that probabilities with finite support are dense in $\mathcal{P}(\mathbb{R})$. See Theorem 6.3 from Probability Measures on Metric Spaces by K.R.Parthasarathy.

I just want to know if this Theorem extended for rationals, that is probabilities having rational mass at finitly many rational points are dense in $\mathcal{P}(\mathbb{R})$

Then how to show that?