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The orbital evolution of more than 22000 Jupiter-crossing objects under the gravitational influence of planets was investigated. We found that the mean collision probabilities of Jupiter-crossing objects (from initial orbits close to the orbit of a comet) with the terrestrial planets can differ by more than two orders of magnitude for different comets. For initial orbital elements close to those of some comets (e.g., 2P and 10P), about 0.1% of objects got Earth-crossing orbits with semi-major axes a < 2 AU and moved in such orbits for more than a Myr (up to tens or even hundreds of Myrs). Results of our runs testify in favor of at least one of these conclusions: (1) the portion of 1-km former trans-Neptunian objects (TNOs) among near-Earth objects (NEOs) can exceed several tens of percent, (2) the number of TNOs migrating inside the solar system could be smaller by a factor of several than it was earlier considered, (3) most of 1-km former TNOs that had got NEO orbits disintegrated into mini-comets and dust during a smaller part of their dynamical lifetimes if these lifetimes are not small.