The Wikipedia article about the H$\alpha$ spectral line states
"it takes nearly as much energy to excite the hydrogen atom's electron from $n = 1$ to $n = 3$ (12.1 eV, via the Rydberg formula) as it does to ionize the hydrogen atom (13.6 eV), ionization is far more probable than excitation to the $ n = 3$ level"
Since 12.1 eV < 13.6 eV, more energy is required to ionize the atom then to excite it to the n=3 level. Hence shouldn't excitation to the n = 3 level be more probable?