We study three CME/ICME events (2008 June 1-6, 2009 February 13-18, 2010 April 3-5) tracked from Sun to 1 AU in remote-sensing observations of STEREO Heliospheric Imagers and in situ plasma and magnetic field measurements. We focus on the ICME propagation in IP space that is governed by two forces, the propelling Lorentz force and the drag force. We address the question at which heliospheric distance range the drag becomes dominant and the CME gets adjusted to the solar wind flow. To this aim we analyze speed differences between ICMEs and the ambient solar wind flow as function of distance. The evolution of the ambient solar wind flow is derived from ENLIL 3D MHD model runs using different solar wind models, namely Wang-Sheeley-Arge (WSA) and MHD-Around-A-Sphere (MAS). Comparing the measured CME kinematics with the solar wind models we find that the CME speed gets adjusted to the solar wind speed at very different heliospheric distances in the three events under study: from below 30 Rs, to beyond 1 AU, depending on the CME and ambient solar wind characteristics. ENLIL can be used to derive important information about the overall structure of the background solar wind, providing more reliable results during times of low solar activity than during times of high solar activity. The results from this study enable us to get a better insight into the forces acting on CMEs over the IP space distance range, which is an important prerequisite in order to predict their 1 AU transit times.