New multimeter probes don't fit my multimeter
It's to meet safety standards that require the "male" part to be insulated so you won't shock yourself if you touch the probe and it's not plugged in. 

It's possible (advisable or not is another question) to modify the probes with an X-Acto knife or box cutter so they will fit your multimeter. 



The ideal solution is to replace your multimeter with a new one that supports the safer probes, at least from the pov of the regulations and the manufacturers of multimeters. 

Edit: Re your added photos, check to make sure the inside is the same and the only thing keeping it from mating is the sheath. Here is the inside of the ones I have modified for an older Uni-T multimeter (used only for low voltage &lt; 30V):