In machine learning, contamination refers to situations where testing data leak into the training set. The issue is particularly relevant for the evaluation of the performance of Large Language Models (LLMs), which are generally trained on gargantuan, and generally opaque, corpora of text scraped from the world wide web. Developing tools to detect contamination is therefore crucial to be able to fairly and properly track the evolution of the performance of LLMs. To date, only a few recent studies have attempted to address the issue of quantifying and detecting contamination in short text sequences, such as those commonly found in benchmarks. However, these methods have limitations that can sometimes render them impractical. In the present paper, we introduce LogProber, a novel, efficient algorithm that we show to be able to detect contamination in a black box setting that tries to tackle some of these drawbacks by focusing on the familiarity with the question rather than the answer. Here, we explore the properties of the proposed method in comparison with concurrent approaches, identify its advantages and limitations, and illustrate how different forms of contamination can go undetected depending on the design of the detection algorithm.