For outcomes k in 0 to K, slope vector a, intercept vector c, and latent ability vector theta,
the response probability function is
$$\mathrm P(\mathrm{pick}=0|a,c,\theta) = 1- \mathrm P(\mathrm{pick}=1|a,c_1,\theta)
$$
$$\mathrm P(\mathrm{pick}=k|a,c,\theta) = \frac{1}{1+\exp(-(a\theta + c_k))} - \frac{1}{1+\exp(-(a\theta + c_{k+1}))}
$$
$$\mathrm P(\mathrm{pick}=K|a,c,\theta) = \frac{1}{1+\exp(-(a\theta + c_K))}
$$