Detecting deposits of amyloid beta fibrils in the brain is of paramount importance for an early diagnosis of Alzheimer's disease. A number of PET tracers have been developed for amyloid imaging but many suffer from poor specificity and large signal to background ratio. Design of tracers with specificity and improved binding affinity requires the knowledge about various possible binding sites in the amyloid beta fibril available for the tracers and the dielectric nature of the local microenvironment of these sites. In this study we investigate the local structure of fibrils using two important probes, namely Thioflavin T (a fluorescent probe) and AZD2184 (a PET tracer). The target structures for amyloid-β (1-42) fibril are based on reported NMR solution models. By explicitly considering the effect of fibril flexibility on the available binding sites for all these models, the binding affinity of these probes has been investigated. The binding profiles of AZD2184 and Thioflavin T were studied by molecular docking and molecular dynamics simulation methods. The two compounds were found to bind at the same sites of the fibril, three of which are within the fibril and one is on the two sides of the Met35 residue on the surface. The binding affinity of AZD2184 and Thioflavin T is found to be higher at the core sites than on the surface due to more contact residues. The binding affinity of AZD2184 is much higher than that of Thioflavin T at every site due to electrostatic interaction and spatial restriction, which is in good agreement with experimental observation. However, the structural change of Thioflavin T is much more significant than that of AZD2184, which is the chemical basis for its usage as a fluorescent probe. The ramifications of these results for the design and optimization of PET radioligands and fluorescent probes are briefly discussed.