How can evaluate the significance of unbalanced variables?

We have a questionnaire which has a question with three options: "a", "b", and "c". All participants are allowed to choose one of these three options.

"a" represents the condition "X" and, "b" and "c" both represent the condition "Y". Our goal is to compare the condition "X" with the condition "Y". Since we have uneven numbers of options in two conditions, how we can evaluate the significance of the preferred option over other options? In other words, if one option is more selected by participants than other options, how can we prove that this preference is inferentially significant?

My data will be something like this:

Participant 1_______0___________0__________1
Participant 2_______1___________0__________0
Participant 3_______1___________0__________0
Participant 4_______0___________1__________0

And how can I use your suggestion in SPSS?

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Omega Contributor
What is you sample size?

One-sample Fisher's exact test, where you compare the proportion to '0' or some number of interest. Similarly liked used in one-sample ttest.