I will talk about zeros of Gaussian Analytic Functions of the form $f(z) = \sum c_k z^k$ with independent standard complex normal coefficients and conditioned by the event that $|f(0)|^2=t$. The probability law of the zero set of $f(z)$ can be derived from that of the spectrum of random sub-unitary matrices. I will explain how this link can be used to obtain the full conditional distribution of radial zero counting function in terms of a $q$-series and use asymptotic expansions of the $q$-series to prove asymptotic normality of the counting function, develop precise large deviation estimates and asymptotic expansion of the conditional hole probability. It turns out that to leading order, the conditional hole probability does not depend on parameter $t$ for $t>0$ and coincides with the hole probability for unconditioned GAF of the form $\sum \sqrt{k+1} c_k z^k$. My talk is based on joint work with Yan Fyodorov and Thomas Prellberg.