= Solution
The two <probabilities> concern different <quantum measurements>, so there is no requirement that they match or that one bound the other. The spatial interval $[0,L/3]$ contains little of the state: its <probability density> is smallest near zero and increases towards $L$. By contrast, the positive <ground state> extends across the whole well. It has substantial same-sign overlap with the positive linear <wavefunction>, with no cancellation between lobes in the overlap <integral>. The right panel of the figure in <past-exam-of-the-short-options-paper-of-the-physics-prelims-of-the-university-of-oxford/2019/s3/1/b/solution> illustrates these two amplitudes and marks the small position interval.
Consequently a large global <ground-state probability> can coexist with a small probability of finding the particle in the left third. This is not because the <ground state> is spatially confined to that third; a ground-state particle can be found throughout the well. In operator language the two events are projections onto a spatial subspace and onto one <energy eigenstate>, respectively.
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