  We have examined the available latest SPS data on $J/\psi$ suppression in
Pb+Pb and In+In collisions at 158 A GeV. Our employed model, with parameters
fixed by $p$-$p$ and $p$-nucleus collisions, gives excellent description of
NA50 and NA60 data on centrality dependence of $J/\psi$ suppression. The model
is then applied to predict the centrality dependence of $J/\psi$ production in
Au+Au collisions at FAIR energy domain. A much larger suppression of $J/\psi$
is predicted. In addition the possible effects of a baryon rich medium on
$J/\psi$ production is also investigated.
