Here is an example: In a conversation, one is asked their opinion regarding a decision, but the decision has already been made—so the individual being asked is led to believe (falsely) that their opinion might have an impact on the outcome.
"Jane [falsely believed her opinion was considered] when her boss asked her who she thought was the best candidate for a job; however, she was not aware that her boss had already selected a candidate to hire."
Or perhaps there is a word meaning "to believe one's opinion is being considered" and the proper use would be to add "falsely" before that word.