Copy number variations (CNVs) are widely known to be an important mediator for diseases and traits. The development of high-throughput sequencing (HTS) technologies has provided great opportunities to identify CNV regions in mammalian genomes. In a typical experiment, millions of short reads obtained from a genome of interest are mapped to a reference genome. The mapping information can be used to identify CNV regions. One important challenge in analyzing the mapping information is the large fraction of reads that can be mapped to multiple positions. Most existing methods either only consider reads that can be uniquely mapped to the reference genome, or randomly place a read to one of its mapping positions. Therefore, these methods have low power to detect CNVs located within repeated sequences. In this study, we propose a probabilistic model, CNVeM, that utilizes the inherent uncertainty of read mapping. We use maximum likelihood to estimate locations and copy numbers of copied regions, and implement an expectation-maximization (EM) algorithm. One important contribution of our model is that we can distinguish between regions in the reference genome that differ from each other by as little as 0.1%. As our model aims to predict the copy number of each nucleotide, we can predict the CNV boundaries with high resolution. We apply our method to simulated datasets and achieve higher accuracy compared to CNVnator. Moreover, we apply our method to real data from which we detected known CNVs. To our knowledge, this is the first attempt to predict CNVs at nucleotide resolution, and to utilize uncertainty of read mapping.