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We first provide a formula to calculate the probability of occurrence ofdifferent configurations (formation probabilities) in a generic free fermionsystem. We then study the scaling of these probabilities with respect to thesize in the case of critical transverse-field XY-chain in the $\sigma^z$ bases.In the case of the transverse field Ising model, we show that all the "crystal"configurations follow the formulas expected from conformal field theory (CFT).In the case of critical $XX$ chain, we show that the only configurations thatfollow the formulas of the CFT are the ones which respect the filling factor ofthe system. By repeating all the calculations in the presence of open andperiodic boundary conditions we find further support to our classification ofdifferent configurations. Using the developed technique, we also study Shannoninformation of a subregion in our system. In this respect we distinguishparticular configurations that are more important in the study of the scalinglimit of the Shannon information of the subsystem. Finally, we study theevolution of formation probabilities, Shannon information and Shannon mutualinformation after a quantum quench in free fermion system. In particular, forthe intial state considered in this paper, we demonstrate that the Shannoninformation after quantum quench first increases with the time and thensaturates at time $t^*=\frac{l}{2}$, where $l$ is the size of the subsystem.

Formation probabilities and Shannon information and their time evolution after quantum quench in transverse-field XY-chain