An　efficient　post-processing　simulation　method　is　proposed　to　estimate　small　failure　probabilities　of　stochastic　dynamic　structures　involving　the　inherent　randomness　of　structural　physical-geometrical　parameters　and　external　excitations.　To　extract　a　small　failure　probability,　the　proposed　method　introduces　an　intermediate　event　to　represent　the　realizations　of　extreme　structural　response　in　the　tail　of　distribution.　With　the　aid　of　this　intermediate　event,　structural　failure　probability　is　reformulated　as　a　product　of　the　event＇s　occurrence　probability　and　the　conditional　exceedance　probability　of　extreme　response　when　the　event　occurs.　The　latter　corresponds　to　a　distribution　of　extreme　response　under　the　condition　of　the　intermediate　event,　referred　to　as　the　conditional　extreme　value　distribution　(CEVD).　Accordingly,　the　proposed　method　is　termed　the　CEVD　method.　To　reconstruct　the　CEVD,　a　truncated　shifted　generalized　lognormal　distribution　model　is　employed.　Bayesian　estimation　method　is　utilized　to　determine　the　two　shape　parameters　of　this　model　based　on　the　samples　of　both　original　extreme　value　distribution　and　CEVD,　where　the　CEVD　samples　are　generated　by　Markov　chain　Monte　Carlo　sampling.　The　efficiency　and　accuracy　of　the　proposed　method　are　demonstrated　through　two　numerical　examples　considering　seismic　reliability　analyses　of　a　10-story　nonlinear　frame　and　a　soil-foundation-structure　interaction　system.　©　2023