We report radio observations of two stripped-envelope supernovae (SNe), 2010O and 2010P, which exploded within a few days of each other in the luminous infrared galaxy Arp 299. Whilst SN 2010O remains undetected at radio frequencies, SN 2010P was detected (with an astrometric accuracy better than 1 milli arcsec in position) in its optically thin phase in epochs ranging from similar to 1 to similar to 3 yr after its explosion date, indicating a very slow radio evolution and a strong interaction of the SN ejecta with the circumstellar medium. Our late-time radio observations towards SN 2010P probe the dense circumstellar envelope of this SN, and imply M [M-circle dot yr(-1)]/upsilon(wind) [10 km s(-1)] = (3.0 - 5.1) x 10(-5), with a 5 GHz peak luminosity of similar to 1.2 x 10(27) erg s(- 1) Hz(- 1) on day similar to 464 after explosion. This is consistent with a Type IIb classification for SN 2010P, making it the most distant and most slowly evolving Type IIb radio SN detected to date.