PlotRange is the option you need:
nTrueTable2 = {"pTT", "pTF", "pFT", "pFF"};
currentPs = {{{1/4, 1/4}, {1/4, 1/4}}, {{1/9, 1/9}, {7/18, 7/18}}, {{2/27, 4/27}, {23/54, 19/54}}, {{2/27, 4/27}, {10/27, 11/27}}};
(BarChart[#, ChartLabels -> Automatic, ImageSize -> Small, PlotRange -> {Automatic, {0, 0.5}}] & /@ (Association[
Table[nTrueTable2[[i]] -> #[[i]], {i, 4}]] & /@Flatten /@ currentPs)) // Row[#, " "] &
