Particle-particle interactions are of paramount importance in every multi-body system as they determine the collective behaviour and coupling strength. Many well-known interactions like electro-static, van der Waals or screened Coulomb, decay exponentially or with negative powers of the particle spacing $r$. Similarly, hydrodynamic interactions between particles undergoing Brownian motion decay as $1/r$ in bulk, and are assumed to decay in small channels. Such interactions are ubiquitous in biological and technological systems. Here I confine multiple particles undergoing Brownian motion in narrow, microfluidic channels and study their coupling through hydrodynamic interactions. Our experiments show that the hydrodynamic particle-particle interactions are distance-independent in these channels. We also show that these interactions affect actively propelled particles via electrophoresis or gravity, resulting in non-linear transport phenomena. These findings are of fundamental importance for understanding transport of dense mixtures of particles or molecules through finite length, water-filled channels or pore networks.