Suppose $Ax=b$ is a linear system and A is a $n \times n$ matrix and vector $b \neq 0$. Suppose all numbers $a_i$ in $A$ and $b_i$ in $b$ belong to $\mathbb{Z}$ and suppose they are in a fixed range such that $|a_i|<c$ and $|b_i|<c$ with c a certain natural number. Question: what is the probability that $Ax=b$ has no solutions (in $\mathbb{Q}$ obv) ?
NOTE: For my $real$ purpose it suffices an answer when $A$ is a $3\times3$ matrix and c=10 FWIW.
Thanks.