Long-range correlations observed in high-multiplicity p+p and p+Pb collisions resemble correlation structures seen in heavy-ion collisions, where they are commonly interpreted as signatures of hydrodynamic collective response. Before extending this interpretation to smaller systems, it is necessary to identify contributions that can arise without hydrodynamic evolution, such as those induced by exact global conservation laws, whose relative importance increases in finite-multiplicity systems. In this talk, I will present a unified conditional-probability framework for relativistic systems in which conditioning on additive conservation laws simultaneously yields equilibrium occupation statistics and global conservation-induced correlations. The one-mode conditional law gives the Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac distributions at leading saddle order, while the two-mode law produces the leading finite-rank covariance induced by exact conservation. This structure allows the construction of observables orthogonal to selected conserved quantities, whose leading conservation-induced covariance vanishes by construction. In small collision systems, where conservation effects are less suppressed by multiplicity, this provides a direct way to separate conservation-aligned and conservation-orthogonal contributions to long-range correlations. The construction will be illustrated using PYTHIA8/Angantyr-generated p+Pb events and its implications for interpreting collectivity in small systems will be discussed.