In the wikipedia article https://en.wikipedia.org/wiki/Principal_bundle the definition of a principal $G-$bundle $\pi:P\rightarrow X$ demands that the action of $G$ on $P$ to be free and transitive.
If I take the trivial $G$ bundle on $X$, that is the projection $X\times G\rightarrow X$ with the action $(x,g)h=(x,gh)$ then this action is not transitive. Indeed, if we take a couple $(x_1,g_1)$ and $(x_2,g_2)$ then there is no $h\in G$ such that $(x_1,g_1)h=(x_2,g_2)$ unless $x_1=x_2$ and in that case $h=g_1^{-1}g_2$.
Where is the problem here? the transitivity condition is not really important in the definition ?