The probe wires must be soldered to the probe tips to be of any value whatsoever. Glue and tape are useless patches.
With that said, to solder them, you must be able to disassemble the tip from the plastic handle. Some tips are screwed into the plastic some are press-fit. The repaired wire must run through the plastic handle for best results.
It may be significantly easier to buy new probe leads.
Some meters are so inexpensive, that buying a whole new meter may be your best bet.
Thanks,
Bill