What is the best way for an 11C to reclassify to 17C? What is the likelihood of reclassifying?

It's an application MOS, you have to apply. If you don't have some type of experience in programming or computer science classes you're probably not going to be competitive to be selected..

MINIMUM REQUIREMENTS:
A physical demands rating of moderate (Gold).
A physical profile of 222221.
Qualifying scores: a minimum score of 110 in aptitude area for GT and a minimum score of 112 in aptitude area ST on ASVAB tests administered on and after 1 April 2014.
A high school graduate or equivalent prior to entry on active duty.
Never been a member of the U.S. Peace Corps, except as specified in AR 614-200 (para 3-2).
No information in military personnel, Provost Marshal, intelligence, or medical records that would prevent the granting of a security eligibility under AR 380-67 (para 2-4).
No record of conviction by court-martial.
No record of conviction by a civil court for any offense other than minor traffic violations.
Must be a U.S. citizen.
The Soldier must have a SECRET clearance to apply but they must meet interim TOP SECRET (TS) Sensitive Compartmented Information (SCI) access eligibility requirements prior to course attendance and to be awarded MOS, then final adjudication to maintain MOS.

You need to speak to your career counselor, they will have your answers.