Can you leave a past employer off of your resume if you only served the probationary period?

You're under no obligation to list all your previous employers on your resume. In fact, it's generally a good idea to only list jobs that you think help make you more qualified for the position you're applying for... Just be prepared to explain any gaps in your resume during an interview or in a cover letter.

The potential risk in leaving some of your job history off your resume is that the employer will notice the "hole" in the timeline and it will look suspicious. They might wonder what you were doing during this period.

Be careful about leaving anything out for the most recent ten year period. For the past two assignments give year and month of beginning and end of assignment. Beyond 10 years or so, you can be very broad. But, don't quibble or equivocate or downright lie. It may be considered grounds for termination. For higher level assignments, always assume that a full check of all credentials and references will be done. Otherwise the recruiting firm really hasn't serviced the client properly. Any negatives (and most of us have at least one glitch in our careers) can be handled verbally (best) or in the cover letter. Be careful. It makes a very bad impression indeed if it emerges that you are trying to hide something. Don't make the mistake of assuming that a potential employer is stupid and won't spot a gap in your record.